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All questions of August Week 3 for JEE Exam
A bar magnet of magnetic moment 1.5 J/T lies parallel to the direction of a uniform magnetic field of 0.22 T. What is the torque acting on it?- a)-0.3J
- b)0.23J
- c)0.0J
- d)0.3J
Correct answer is option 'B'. Can you explain this answer?
A bar magnet of magnetic moment 1.5 J/T lies parallel to the direction of a uniform magnetic field of 0.22 T. What is the torque acting on it?
a)
-0.3J
b)
0.23J
c)
0.0J
d)
0.3J
|
Preeti Iyer answered |
Answer :-
Solution :- torque when 
=180°
=180°
= 1.5 × 0.22 × sin 180°
= 0.33 × 0 = 0 Nm
A toroid wound with 60.0 turns/m of wire carries a current of 5.00 A. The torus is iron, which has a magnetic permeability of μm=5000μ0 under the given conditions. H and B inside the iron are- a)340AT/m,2.88T
- b)340AT/m,1.88T
- c)380AT/m,1.98T
- d)300AT/m,1.88T
Correct answer is option 'D'. Can you explain this answer?
A toroid wound with 60.0 turns/m of wire carries a current of 5.00 A. The torus is iron, which has a magnetic permeability of μm=5000μ0 under the given conditions. H and B inside the iron are
a)
340AT/m,2.88T
b)
340AT/m,1.88T
c)
380AT/m,1.98T
d)
300AT/m,1.88T
|
Neha Sharma answered |
B=B0+Bm
= μ0nI+ μmnI
=nI(μ+ μm)
=60x5(5000μ0+ μ0)
B=300(5001μ0)
B=1.88T
H=B/μm
=300x5001μ0/5000μ
=300AT
= μ0nI+ μmnI
=nI(μ+ μm)
=60x5(5000μ0+ μ0)
B=300(5001μ0)
B=1.88T
H=B/μm
=300x5001μ0/5000μ
=300AT
Which of the following statements about earth's magnetism is correct- a)The earth behaves as a magnet with the magnetic field pointing approximately from the geographic south-west to the north-east.
- b)The earth behaves as a magnet with the magnetic field pointing approximately from the geographic south-east to the north-west.
- c)The earth behaves as a magnet with the magnetic field pointing approximately from the geographic east to the west.
- d)The earth behaves as a magnet with the magnetic field pointing approximately from the geographic south to the north.
Correct answer is option 'D'. Can you explain this answer?
Which of the following statements about earth's magnetism is correct
a)
The earth behaves as a magnet with the magnetic field pointing approximately from the geographic south-west to the north-east.
b)
The earth behaves as a magnet with the magnetic field pointing approximately from the geographic south-east to the north-west.
c)
The earth behaves as a magnet with the magnetic field pointing approximately from the geographic east to the west.
d)
The earth behaves as a magnet with the magnetic field pointing approximately from the geographic south to the north.
|
Sarthak Bansal answered |
According to recent researches the magnetic field of earth is considered due to a large bar magnet situated in earth's core.
It is considered that the north pole of this large magnet is situated at the geographical south of earth and vice versa and as the magnetic field due to a bar magnet is from north pole to south pole of the maget thus the earth's magnetic field is considered from geographical south to geographical north which are respectively north and south poles of the bar magnet.
It is considered that the north pole of this large magnet is situated at the geographical south of earth and vice versa and as the magnetic field due to a bar magnet is from north pole to south pole of the maget thus the earth's magnetic field is considered from geographical south to geographical north which are respectively north and south poles of the bar magnet.
A short bar magnet has a magnetic moment of 0.48 J/T .Magnetic field produced by the magnet at a distance of 10 cm from the centre of the magnet on the axis has a direction and magnitude of .- a)1.06 G along S-N direction.
- b)0.96 G along S-N direction.
- c)0.86 G along S-N direction.
- d)0.76 G along S-N direction.
Correct answer is option 'B'. Can you explain this answer?
A short bar magnet has a magnetic moment of 0.48 J/T .Magnetic field produced by the magnet at a distance of 10 cm from the centre of the magnet on the axis has a direction and magnitude of .
a)
1.06 G along S-N direction.
b)
0.96 G along S-N direction.
c)
0.86 G along S-N direction.
d)
0.76 G along S-N direction.
|
Tanuja Kapoor answered |
Here M=0.48JT−1,d=10cm=0.1m
On axis,
B= (μ0/4π)(2M/d3)=10−7×(2×0.48/0.13)=0.96×10−4T
On axis,
B= (μ0/4π)(2M/d3)=10−7×(2×0.48/0.13)=0.96×10−4T
Find slope of normal to the curve y=5x2-10x + 7 at x=1- a)not defined
- b)-1
- c)1
- d)zero
Correct answer is option 'A'. Can you explain this answer?
Find slope of normal to the curve y=5x2-10x + 7 at x=1
a)
not defined
b)
-1
c)
1
d)
zero
|
|
Neha Sharma answered |
y = 5x2 - 10x + 7
dy/dx = 10x - 10
(At x = 1) 10(1) - 10
m1 = 0
As we know that slope, m1m2 = -1
=> 0(m2) = -1
m2 = -1/0 (which is not defined)
dy/dx = 10x - 10
(At x = 1) 10(1) - 10
m1 = 0
As we know that slope, m1m2 = -1
=> 0(m2) = -1
m2 = -1/0 (which is not defined)
In the magnetic meridian of a certain place, the horizontal component of the earth’s magnetic field is 0.26G and the dip angle is 600. What is the magnetic field of the earth at this location- a)0.65G
- b)0.62G
- c)0.58G
- d)0.52G
Correct answer is option 'D'. Can you explain this answer?
In the magnetic meridian of a certain place, the horizontal component of the earth’s magnetic field is 0.26G and the dip angle is 600. What is the magnetic field of the earth at this location
a)
0.65G
b)
0.62G
c)
0.58G
d)
0.52G
|
Om Desai answered |
The earth's magnetic field is Be and its horizontal and vertical components are He and Hv
cosθ= He/Be
∴cos60o= (0.26×10−4/ Be )T
⇒Be=(0.26×10−4)/ (½)=0.52×10−4T=0.52G
cosθ= He/Be
∴cos60o= (0.26×10−4/ Be )T
⇒Be=(0.26×10−4)/ (½)=0.52×10−4T=0.52G
A Rowland ring of mean radius 15 cm has 3500 turns of wire wound on a ferromagnetic core of relative permeability 800. What is the magnetic field B in the core for a magnetising current of 12 A ?- a)4.48 T
- b)5.48 T
- c)44.8 T
- d)48 T
Correct answer is option 'A'. Can you explain this answer?
A Rowland ring of mean radius 15 cm has 3500 turns of wire wound on a ferromagnetic core of relative permeability 800. What is the magnetic field B in the core for a magnetising current of 12 A ?
a)
4.48 T
b)
5.48 T
c)
44.8 T
d)
48 T
|
Sankar Singh answered |
Calculation of Magnetic Field B in the Core
Given:
Mean radius of Rowland ring, r = 15 cm = 0.15 m
Number of turns of wire, N = 3500
Relative permeability of ferromagnetic core, μr = 800
Magnetising current, I = 12 A
The magnetic field B in the core of Rowland ring can be calculated using the formula:
B = (μ0 * N * I) / (2 * r)
where, μ0 is the permeability of free space
μ0 = 4π * 10^-7 Tm/A
Substituting the given values in the formula,
B = (4π * 10^-7 Tm/A * 3500 * 12 A) / (2 * 0.15 m)
B = 4.48 T
Therefore, the magnetic field B in the core of Rowland ring for a magnetising current of 12 A is 4.48 T, which is option A.
Given:
Mean radius of Rowland ring, r = 15 cm = 0.15 m
Number of turns of wire, N = 3500
Relative permeability of ferromagnetic core, μr = 800
Magnetising current, I = 12 A
The magnetic field B in the core of Rowland ring can be calculated using the formula:
B = (μ0 * N * I) / (2 * r)
where, μ0 is the permeability of free space
μ0 = 4π * 10^-7 Tm/A
Substituting the given values in the formula,
B = (4π * 10^-7 Tm/A * 3500 * 12 A) / (2 * 0.15 m)
B = 4.48 T
Therefore, the magnetic field B in the core of Rowland ring for a magnetising current of 12 A is 4.48 T, which is option A.
The equation of the normal to the curve x2 = 4y which passes through the point (1, 2) is.- a)x + y – 3 = 0
- b)4x – y = 2
- c)4x – 2y = 0
- d)4x – 3y + 2= 0
Correct answer is option 'B'. Can you explain this answer?
The equation of the normal to the curve x2 = 4y which passes through the point (1, 2) is.
a)
x + y – 3 = 0
b)
4x – y = 2
c)
4x – 2y = 0
d)
4x – 3y + 2= 0
|
Sushil Kumar answered |
h2 = 4k
slope of normal=−1/(dy/dx) = −2h
equation of normal(y − k)= −2h(x−h)
k = 2 + 2/h(1 − h)
(h2) / 4 = 2 + 2/h (1 − h)
h = 2, k = 1
equation of line (y - 1)= -1(x - 2)
x + y = 3
slope of normal=−1/(dy/dx) = −2h
equation of normal(y − k)= −2h(x−h)
k = 2 + 2/h(1 − h)
(h2) / 4 = 2 + 2/h (1 − h)
h = 2, k = 1
equation of line (y - 1)= -1(x - 2)
x + y = 3
A cube-shaped permanent magnet is made of a ferromagnetic material with a magnetization M of about The side length is 2 cm. Magnetic dipole moment of the magnet is.
- a)5Am2
- b)3Am2
- c)4Am2
- d)6Am2
Correct answer is option 'C'. Can you explain this answer?
A cube-shaped permanent magnet is made of a ferromagnetic material with a magnetization M of about The side length is 2 cm. Magnetic dipole moment of the magnet is.
a)
5Am2
b)
3Am2
c)
4Am2
d)
6Am2
|
Infinity Academy answered |
Correct Answer :- C
Explanation : Magnetic Moment = Magnetization × Volume
Side of cube = 20 cm
= 0.2 m
= 500 × 0.2 × 0.2 × 0.2
= 4Am2
Correct unit of Bohr magneton is- a)T
- b)T/J
- c)J/T
- d)J
Correct answer is option 'C'. Can you explain this answer?
Correct unit of Bohr magneton is
a)
T
b)
T/J
c)
J/T
d)
J
|
|
Sushil Kumar answered |
The Bohr magneton μB is a physical constant and the natural unit for expressing the magnetic moment of an electron caused by either its orbital or spin angular momentum.
μB= eℏ/2me
where e is the elementary charge, ℏ is the reduced Planck's constant, me is the electron rest mass.
The value of Bohr magneton in SI units is 9.27400968(20)×10−24JT−1
μB= eℏ/2me
where e is the elementary charge, ℏ is the reduced Planck's constant, me is the electron rest mass.
The value of Bohr magneton in SI units is 9.27400968(20)×10−24JT−1
A short bar magnet of magnetic moment 5.25×10−2JT−1 is placed with its axis perpendicular to the earth’s field direction. At what distance from the centre of the magnet, the resultant field is inclined at 45 with earth’s field on its normal bisector . Magnitude of the earth’s field at the place is given to be 0.42 G. Ignore the length of the magnet in comparison to the distances involved.- a)5.5 cm
- b)7.0 cm
- c)6.0 cm
- d)5 cm
Correct answer is option 'D'. Can you explain this answer?
A short bar magnet of magnetic moment 5.25×10−2JT−1 is placed with its axis perpendicular to the earth’s field direction. At what distance from the centre of the magnet, the resultant field is inclined at 45 with earth’s field on its normal bisector . Magnitude of the earth’s field at the place is given to be 0.42 G. Ignore the length of the magnet in comparison to the distances involved.
a)
5.5 cm
b)
7.0 cm
c)
6.0 cm
d)
5 cm
|
|
Nandini Iyer answered |
According to the question, the resultant field is inclined at 45o with earth's magnetic field.
tanθ=BH/B
θ=45o
tanθ=1=BH/B
BH=B= μoM/4πr3
Given, B= 0.42×10−4T
M=5.25×10−2J/T
Therefore,0.42+10−4=10−7×[(5.25×10−2)/r3]
r3=12.5×10−5=125×10−6
r=5×10−2m = 5 cm
tanθ=BH/B
θ=45o
tanθ=1=BH/B
BH=B= μoM/4πr3
Given, B= 0.42×10−4T
M=5.25×10−2J/T
Therefore,0.42+10−4=10−7×[(5.25×10−2)/r3]
r3=12.5×10−5=125×10−6
r=5×10−2m = 5 cm
A cube-shaped permanent magnet is made of a ferromagnetic material with a magnetization M of about The side length is 2 cm. Magnetic field due to the magnet at a point 10 cm from the magnet along its axis is
- a)0.003 T
- b)0.002 T
- c)0.004 T
- d)0.001 T
Correct answer is option 'D'. Can you explain this answer?
A cube-shaped permanent magnet is made of a ferromagnetic material with a magnetization M of about The side length is 2 cm. Magnetic field due to the magnet at a point 10 cm from the magnet along its axis is
a)
0.003 T
b)
0.002 T
c)
0.004 T
d)
0.001 T
|
|
Riya Banerjee answered |
Correct Answer :- d
Explanation : μtotal = MV
= (8*105)(2*10-2)
= 6A m2
Magnetic field on the axis of a current loop with magnetic material μtotal is:
B = μ0 μtotal / (2π(x2 + a2)1/2
B = (4π*10-7)(6) / [2π(0.1)]
= 1 * 10-3 T
= 0.001 T
For diamagnetic materials- a)additional field caused by atoms is always parallel in direction to that of the external field
- b)additional field caused by atoms is always perpendicular in direction to that of the external field
- c)additional field caused by atoms is always in same direction as that of the external field
- d)additional field caused by atoms is always opposite in direction to that of the external field
Correct answer is option 'D'. Can you explain this answer?
For diamagnetic materials
a)
additional field caused by atoms is always parallel in direction to that of the external field
b)
additional field caused by atoms is always perpendicular in direction to that of the external field
c)
additional field caused by atoms is always in same direction as that of the external field
d)
additional field caused by atoms is always opposite in direction to that of the external field
|
Ahtesham Rashid answered |
It is because when we make a group of electrons inside the material it is called domain. So when we apply external magnetic field on the material. Those domains start to align themselves in the direction of magnetic field. BUT NOT ALL DOMAINS ALIGN THEMSELVES IN THAT DIRECTION. So option D is correct.
If a magnet is suspended over a container of liquid air, it attracts droplets to its poles. The droplets contain only liquid oxygen and no nitrogen because- a)oxygen is ferromagnetic whereas nitrogen is diamagnetic
- b)oxygen is ferrimagnetic whereas nitrogen is diamagnetic
- c)oxygen is diamagnetic whereas nitrogen is paramagnetic
- d)oxygen is paramagnetic whereas nitrogen is diamagnetic
Correct answer is option 'D'. Can you explain this answer?
If a magnet is suspended over a container of liquid air, it attracts droplets to its poles. The droplets contain only liquid oxygen and no nitrogen because
a)
oxygen is ferromagnetic whereas nitrogen is diamagnetic
b)
oxygen is ferrimagnetic whereas nitrogen is diamagnetic
c)
oxygen is diamagnetic whereas nitrogen is paramagnetic
d)
oxygen is paramagnetic whereas nitrogen is diamagnetic
|
|
Anaya Patel answered |
If a magnet is suspended over a container of liquid air, it attracts droplets to its poles. The droplets contain only liquid oxygen; even though nitrogen is the primary constituent of air, it is not attracted to the magnet. Explain what this tells you about the magnetic susceptibilities of oxygen and nitrogen, and explain why a magnet in ordinary, room-temperature air doesn’t attract molecules of oxygen gas to its poles.
For paramagnetic materials- a)orbital and spin magnetic moments of the electrons are of the order of bohr magneton
- b)orbital magnetic moments of the electrons are zero
- c)orbital and spin magnetic moments of the electrons are less than zero
- d)spin magnetic moments of the electrons are zero
Correct answer is option 'A'. Can you explain this answer?
For paramagnetic materials
a)
orbital and spin magnetic moments of the electrons are of the order of bohr magneton
b)
orbital magnetic moments of the electrons are zero
c)
orbital and spin magnetic moments of the electrons are less than zero
d)
spin magnetic moments of the electrons are zero
|
|
Shubham Jain answered |
Paramagnetic materials are those materials that are weakly attracted by a magnetic field. They have unpaired electrons in their outermost shell, which causes a net magnetic moment due to the spin and orbital motion of the electrons.
Orbital and Spin Magnetic Moments:
- Orbital magnetic moment: It is the magnetic moment of an electron due to its motion around the nucleus.
- Spin magnetic moment: It is the magnetic moment of an electron due to its intrinsic spin.
Order of Bohr Magneton:
- Bohr magneton is a unit of magnetic moment, which is equal to approximately 9.27 x 10^-24 joules per tesla.
- The orbital and spin magnetic moments of electrons in paramagnetic materials are of the order of Bohr magneton.
Explanation of Option A:
- Option A states that the orbital and spin magnetic moments of electrons in paramagnetic materials are of the order of Bohr magneton.
- This is correct because the unpaired electrons in paramagnetic materials have a net magnetic moment due to their spin and orbital motion, which is of the order of Bohr magneton.
- This magnetic moment causes the paramagnetic material to be weakly attracted to a magnetic field.
Other Options:
- Option B states that the orbital magnetic moments of electrons in paramagnetic materials are zero, which is incorrect because the unpaired electrons have an orbital magnetic moment.
- Option C states that the orbital and spin magnetic moments of electrons in paramagnetic materials are less than zero, which is incorrect because magnetic moments cannot be negative.
- Option D states that the spin magnetic moments of electrons in paramagnetic materials are zero, which is incorrect because the unpaired electrons have a spin magnetic moment.
Orbital and Spin Magnetic Moments:
- Orbital magnetic moment: It is the magnetic moment of an electron due to its motion around the nucleus.
- Spin magnetic moment: It is the magnetic moment of an electron due to its intrinsic spin.
Order of Bohr Magneton:
- Bohr magneton is a unit of magnetic moment, which is equal to approximately 9.27 x 10^-24 joules per tesla.
- The orbital and spin magnetic moments of electrons in paramagnetic materials are of the order of Bohr magneton.
Explanation of Option A:
- Option A states that the orbital and spin magnetic moments of electrons in paramagnetic materials are of the order of Bohr magneton.
- This is correct because the unpaired electrons in paramagnetic materials have a net magnetic moment due to their spin and orbital motion, which is of the order of Bohr magneton.
- This magnetic moment causes the paramagnetic material to be weakly attracted to a magnetic field.
Other Options:
- Option B states that the orbital magnetic moments of electrons in paramagnetic materials are zero, which is incorrect because the unpaired electrons have an orbital magnetic moment.
- Option C states that the orbital and spin magnetic moments of electrons in paramagnetic materials are less than zero, which is incorrect because magnetic moments cannot be negative.
- Option D states that the spin magnetic moments of electrons in paramagnetic materials are zero, which is incorrect because the unpaired electrons have a spin magnetic moment.
A toroidal solenoid with 500 turns is wound on a ring with a mean radius of 2.90 cm. Find the current in the winding that is required to set up a magnetic field of 0.350 T in the ring if the ring is made of annealed iron Km=1400- a)82.5mA
- b)72.5mA
- c)79.5mA
- d)69.5mA
Correct answer is option 'B'. Can you explain this answer?
A toroidal solenoid with 500 turns is wound on a ring with a mean radius of 2.90 cm. Find the current in the winding that is required to set up a magnetic field of 0.350 T in the ring if the ring is made of annealed iron Km=1400
a)
82.5mA
b)
72.5mA
c)
79.5mA
d)
69.5mA
|
Geetika Shah answered |
Given,
Number of turns, N = 500 turns
Radius of solenoid, r = 2.9
Relative permeability of annealed iron of Km=1400
Permeability of free space, μ0 =4π
The magnetic field, B=0.350 T
Therefore,
μ/μ0= μr
μ= μr x μ0
B= μrμ0NI/2πR
0.350=1400x4x 3.14x500xI/2xπx2.90
I=72.mA
Number of turns, N = 500 turns
Radius of solenoid, r = 2.9
Relative permeability of annealed iron of Km=1400
Permeability of free space, μ0 =4π
The magnetic field, B=0.350 T
Therefore,
μ/μ0= μr
μ= μr x μ0
B= μrμ0NI/2πR
0.350=1400x4x 3.14x500xI/2xπx2.90
I=72.mA
The equation of the tangent line to the curve y = 
which is parallel to the line 4x -2y + 3 = 0 is
- a)80x +40y – 193 = 0
- b)4x – 2y – 3 = 0
- c)80x – 40y + 193 = 0
- d)80x – 40y – 103 = 0
Correct answer is option 'D'. Can you explain this answer?
The equation of the tangent line to the curve y = which is parallel to the line 4x -2y + 3 = 0 is
which is parallel to the line 4x -2y + 3 = 0 isa)
80x +40y – 193 = 0
b)
4x – 2y – 3 = 0
c)
80x – 40y + 193 = 0
d)
80x – 40y – 103 = 0
|
Dabhi Bharat answered |
Given curve y=√5x-3 -2
y+2=√5x-3
dy/dx=5/2×√5x-3
m1=5/2(y+2)
given that line 4x-2y+3=0is parallel to tangent of curve
slope of line m2=2
m1=m2
5/2(y+2)=2
5/4=(y+2)
y=-3/4
from y+2=√5x-3
-3/4+2=√5x-3
5/4=√5x-3
5x=25/16+3
X=73/80
points are p(73/80,-3/4)
equ. of tangent :y-y1=m(x-x1)
y+3/4=2(x-73/80)
80x-73=40y+30
80x-40y-103=0
y+2=√5x-3
dy/dx=5/2×√5x-3
m1=5/2(y+2)
given that line 4x-2y+3=0is parallel to tangent of curve
slope of line m2=2
m1=m2
5/2(y+2)=2
5/4=(y+2)
y=-3/4
from y+2=√5x-3
-3/4+2=√5x-3
5/4=√5x-3
5x=25/16+3
X=73/80
points are p(73/80,-3/4)
equ. of tangent :y-y1=m(x-x1)
y+3/4=2(x-73/80)
80x-73=40y+30
80x-40y-103=0
A short bar magnet placed in a horizontal plane has its axis aligned along the magnetic north-south direction. Null points are found on the axis of the magnet at 14 cm from the centre of the magnet. The earth’s magnetic field at the place is 0.36 G and the angle of dip is zero. What is the total magnetic field on the normal bisector of the magnet at the same distance as the null–point (i.e., 14 cm) from the centre of the magnet? (At null points, field due to a magnet is equal and opposite to the horizontal component of earth’s magnetic field.)- a)0.64 G in the direction of earth’s field.
- b)0.62 G in the direction of earth’s field.
- c)0.54 G in the direction of earth’s field.
- d)0.58 G in the direction of earth’s field.
Correct answer is option 'C'. Can you explain this answer?
A short bar magnet placed in a horizontal plane has its axis aligned along the magnetic north-south direction. Null points are found on the axis of the magnet at 14 cm from the centre of the magnet. The earth’s magnetic field at the place is 0.36 G and the angle of dip is zero. What is the total magnetic field on the normal bisector of the magnet at the same distance as the null–point (i.e., 14 cm) from the centre of the magnet? (At null points, field due to a magnet is equal and opposite to the horizontal component of earth’s magnetic field.)
a)
0.64 G in the direction of earth’s field.
b)
0.62 G in the direction of earth’s field.
c)
0.54 G in the direction of earth’s field.
d)
0.58 G in the direction of earth’s field.
|
Janhavi Kaur answered |
To find the total magnetic field on the normal bisector of the magnet at the same distance as the null point, we need to consider the contributions from both the magnet and the Earth's magnetic field.
1. Magnetic Field due to the Magnet:
The null points on the axis of the magnet indicate that the field due to the magnet is equal and opposite to the horizontal component of the Earth's magnetic field. Therefore, the horizontal component of the magnet's field at the null point is equal to the Earth's magnetic field.
Given that the null point is at a distance of 14 cm from the center of the magnet, we can use the formula for the magnetic field along the axis of a short bar magnet:
B = (μ₀/4π) * (2M/(d³))
Where:
B is the magnetic field
μ₀ is the permeability of free space (4π x 10^-7 Tm/A)
M is the magnetic moment of the magnet
d is the distance from the center of the magnet
Since the null point is at 14 cm from the center, the distance from the center to the null point is 7 cm (0.07 m). The magnetic field due to the magnet at this point is equal to the Earth's magnetic field, which is given as 0.36 G (1 G = 10^-4 T).
2. Total Magnetic Field:
The total magnetic field on the normal bisector at the same distance from the center of the magnet can be found by vector addition of the Earth's magnetic field and the magnetic field due to the magnet.
Since the angle of dip is zero, the Earth's magnetic field is entirely horizontal. Therefore, the total magnetic field will be the vector sum of the Earth's magnetic field and the magnetic field due to the magnet.
The total magnetic field is given by:
B_total = √(B_magnet² + B_earth² + 2B_magnetB_earthcosθ)
Where:
B_magnet is the magnetic field due to the magnet
B_earth is the Earth's magnetic field
θ is the angle between the two fields (which is 180° since they are opposite in direction)
Plugging in the values:
B_total = √((0.36 G)² + (0.36 G)² + 2(0.36 G)(0.36 G)cos180°)
B_total = √(0.1296 G² + 0.1296 G² - 2(0.1296 G²))
B_total = √(0.2592 G² - 0.2592 G²)
B_total = √0 G²
B_total = 0 G
Therefore, the total magnetic field on the normal bisector of the magnet at the same distance as the null point is 0 G. None of the given options (a, b, c, d) match the correct answer.
1. Magnetic Field due to the Magnet:
The null points on the axis of the magnet indicate that the field due to the magnet is equal and opposite to the horizontal component of the Earth's magnetic field. Therefore, the horizontal component of the magnet's field at the null point is equal to the Earth's magnetic field.
Given that the null point is at a distance of 14 cm from the center of the magnet, we can use the formula for the magnetic field along the axis of a short bar magnet:
B = (μ₀/4π) * (2M/(d³))
Where:
B is the magnetic field
μ₀ is the permeability of free space (4π x 10^-7 Tm/A)
M is the magnetic moment of the magnet
d is the distance from the center of the magnet
Since the null point is at 14 cm from the center, the distance from the center to the null point is 7 cm (0.07 m). The magnetic field due to the magnet at this point is equal to the Earth's magnetic field, which is given as 0.36 G (1 G = 10^-4 T).
2. Total Magnetic Field:
The total magnetic field on the normal bisector at the same distance from the center of the magnet can be found by vector addition of the Earth's magnetic field and the magnetic field due to the magnet.
Since the angle of dip is zero, the Earth's magnetic field is entirely horizontal. Therefore, the total magnetic field will be the vector sum of the Earth's magnetic field and the magnetic field due to the magnet.
The total magnetic field is given by:
B_total = √(B_magnet² + B_earth² + 2B_magnetB_earthcosθ)
Where:
B_magnet is the magnetic field due to the magnet
B_earth is the Earth's magnetic field
θ is the angle between the two fields (which is 180° since they are opposite in direction)
Plugging in the values:
B_total = √((0.36 G)² + (0.36 G)² + 2(0.36 G)(0.36 G)cos180°)
B_total = √(0.1296 G² + 0.1296 G² - 2(0.1296 G²))
B_total = √(0.2592 G² - 0.2592 G²)
B_total = √0 G²
B_total = 0 G
Therefore, the total magnetic field on the normal bisector of the magnet at the same distance as the null point is 0 G. None of the given options (a, b, c, d) match the correct answer.
Find the equation of tangent to 
which has slope 2.- a)2x – y = 1
- b)No tangent
- c)y – 2x = 0
- d)y – 2x = 3
Correct answer is option 'B'. Can you explain this answer?
Find the equation of tangent to which has slope 2.
which has slope 2.a)
2x – y = 1
b)
No tangent
c)
y – 2x = 0
d)
y – 2x = 3
|
|
Raghava Rao answered |
Y=1/(x-3)^2
dy/dx=(-1/(x-3)^2)
given slope=2
-1/(x-3)^2 =2
-1/2=(x-3)^2
negative number is not equal to square. so no tangent
dy/dx=(-1/(x-3)^2)
given slope=2
-1/(x-3)^2 =2
-1/2=(x-3)^2
negative number is not equal to square. so no tangent
Which of the following statements about magnetic field lines true?- a)The magnetic field lines of a magnet (or a solenoid) form continuous closed loops
- b)The smaller the number of field lines crossing per unit area, the stronger is the magnitude of the magnetic field B.
- c)The perpendicular to the field line at a given point gives direction of magnetic field
- d)The larger the number of field lines crossing per unit area, the weaker is the magnitude of the magnetic field B.
Correct answer is option 'A'. Can you explain this answer?
Which of the following statements about magnetic field lines true?
a)
The magnetic field lines of a magnet (or a solenoid) form continuous closed loops
b)
The smaller the number of field lines crossing per unit area, the stronger is the magnitude of the magnetic field B.
c)
The perpendicular to the field line at a given point gives direction of magnetic field
d)
The larger the number of field lines crossing per unit area, the weaker is the magnitude of the magnetic field B.
|
Krishna Iyer answered |
Magnetic poles exist in pairs. It is not possible to isolate a north pole or a south pole. Magnetic field lines start from the north pole and go to the south pole and return to the north pole. They form continuous closed loops unlike electric lines of force which do not as an electric monopole, a single charge does exist.
A magnetic needle free to rotate in a vertical plane parallel to the magnetic meridian has its north tip pointing down at 220 with the horizontal. The horizontal component of the earth’s magnetic field at the place is known to be 0.35 G. Determine the magnitude of the earth’s magnetic field at the place.- a)0.48G
- b)0.28G
- c)0.58G
- d)0.38G
Correct answer is option 'D'. Can you explain this answer?
A magnetic needle free to rotate in a vertical plane parallel to the magnetic meridian has its north tip pointing down at 220 with the horizontal. The horizontal component of the earth’s magnetic field at the place is known to be 0.35 G. Determine the magnitude of the earth’s magnetic field at the place.
a)
0.48G
b)
0.28G
c)
0.58G
d)
0.38G
|
Hansa Sharma answered |
We know the horizontal component of earth magnetic field H=R cos θ
Where θ=angle of dip=220 and the value of H=0.35G
So, putting the values respectively R= H/cosθ=0.35/cos22=0.35/0.927=0.377=0.38G
Where θ=angle of dip=220 and the value of H=0.35G
So, putting the values respectively R= H/cosθ=0.35/cos22=0.35/0.927=0.377=0.38G
In which case of comparing solenoid and bar magnet there is no exact similarity?- a)There is a current entering and a current leaving a solenoid
- b)soenoid can be broken into two weaker solenoids
- c)flux lines enter one end of a solenoid
- d)moving a small compass needle in the neighbourhood of a solenoid enables tracing the flux lines
Correct answer is option 'A'. Can you explain this answer?
In which case of comparing solenoid and bar magnet there is no exact similarity?
a)
There is a current entering and a current leaving a solenoid
b)
soenoid can be broken into two weaker solenoids
c)
flux lines enter one end of a solenoid
d)
moving a small compass needle in the neighbourhood of a solenoid enables tracing the flux lines
|
|
Kiran Khanna answered |
Comparing Solenoid and Bar Magnet
Introduction:
Solenoid and bar magnet are two types of magnets that have different properties. However, there are some similarities between them. In this question, we need to identify the case where there is no exact similarity between solenoid and bar magnet.
Answer:
The correct answer is option 'A' - "There is a current entering and a current leaving a solenoid". Let's understand why this is the correct answer.
Solenoid:
A solenoid is a coil of wire that produces a magnetic field when an electric current is passed through it. The magnetic field produced by a solenoid is similar to that of a bar magnet. However, there are some differences.
Bar Magnet:
A bar magnet is a permanent magnet that has a north pole and a south pole. The magnetic field of a bar magnet is uniform and is strongest at the poles.
Comparison:
Now let's compare the two magnets based on the given options.
a) There is a current entering and a current leaving a solenoid:
This is a property unique to solenoids. When an electric current is passed through a solenoid, there is a current entering at one end and a current leaving at the other end. This is because a solenoid is a coil of wire that is wrapped around a core. As a result, the magnetic field produced by a solenoid is concentrated inside the coil and is weaker outside.
b) Solenoid can be broken into two weaker solenoids:
This is a property that is similar to a bar magnet. A bar magnet can be broken into two weaker magnets, each with its own north and south pole. Similarly, a solenoid can be broken into two weaker solenoids, each with its own magnetic field.
c) Flux lines enter one end of a solenoid:
This is a property that is similar to a bar magnet. The magnetic field of a bar magnet is uniform and the flux lines enter at one end and exit at the other end. Similarly, the magnetic field of a solenoid is strongest at the ends and the flux lines enter at one end and exit at the other end.
d) Moving a small compass needle in the neighbourhood of a solenoid enables tracing the flux lines:
This is a property that is similar to a bar magnet. The magnetic field of a bar magnet can be visualized using iron filings or a small compass needle. Similarly, the magnetic field of a solenoid can be visualized using a small compass needle.
Conclusion:
Based on the above comparison, we can see that option 'A' is the correct answer as it is the only option that is unique to solenoids and does not have a similar property in bar magnets.
Introduction:
Solenoid and bar magnet are two types of magnets that have different properties. However, there are some similarities between them. In this question, we need to identify the case where there is no exact similarity between solenoid and bar magnet.
Answer:
The correct answer is option 'A' - "There is a current entering and a current leaving a solenoid". Let's understand why this is the correct answer.
Solenoid:
A solenoid is a coil of wire that produces a magnetic field when an electric current is passed through it. The magnetic field produced by a solenoid is similar to that of a bar magnet. However, there are some differences.
Bar Magnet:
A bar magnet is a permanent magnet that has a north pole and a south pole. The magnetic field of a bar magnet is uniform and is strongest at the poles.
Comparison:
Now let's compare the two magnets based on the given options.
a) There is a current entering and a current leaving a solenoid:
This is a property unique to solenoids. When an electric current is passed through a solenoid, there is a current entering at one end and a current leaving at the other end. This is because a solenoid is a coil of wire that is wrapped around a core. As a result, the magnetic field produced by a solenoid is concentrated inside the coil and is weaker outside.
b) Solenoid can be broken into two weaker solenoids:
This is a property that is similar to a bar magnet. A bar magnet can be broken into two weaker magnets, each with its own north and south pole. Similarly, a solenoid can be broken into two weaker solenoids, each with its own magnetic field.
c) Flux lines enter one end of a solenoid:
This is a property that is similar to a bar magnet. The magnetic field of a bar magnet is uniform and the flux lines enter at one end and exit at the other end. Similarly, the magnetic field of a solenoid is strongest at the ends and the flux lines enter at one end and exit at the other end.
d) Moving a small compass needle in the neighbourhood of a solenoid enables tracing the flux lines:
This is a property that is similar to a bar magnet. The magnetic field of a bar magnet can be visualized using iron filings or a small compass needle. Similarly, the magnetic field of a solenoid can be visualized using a small compass needle.
Conclusion:
Based on the above comparison, we can see that option 'A' is the correct answer as it is the only option that is unique to solenoids and does not have a similar property in bar magnets.
A compass needle free to turn in a horizontal plane is placed at the centre of circular coil of 30 turns and radius 12 cm. The coil is in a vertical plane making an angle of 450 with the magnetic meridian. When the current in the coil is 0.35 A, the needle points west to east. Determine the horizontal component of the earth’s magnetic field at the location- a)0.34G
- b)0.49G
- c)0.29G
- d)0.39G
Correct answer is option 'D'. Can you explain this answer?
A compass needle free to turn in a horizontal plane is placed at the centre of circular coil of 30 turns and radius 12 cm. The coil is in a vertical plane making an angle of 450 with the magnetic meridian. When the current in the coil is 0.35 A, the needle points west to east. Determine the horizontal component of the earth’s magnetic field at the location
a)
0.34G
b)
0.49G
c)
0.29G
d)
0.39G
|
|
Shruti Sarkar answered |
The needle will point along W-E if the result of the earth’s magnetic field and magnetic field due to the coil have a resultant in the W-E direction. This happens if B cos 45o=Earth's field
⟹ (μ0nI/2r) cos45o=(4π×10−7×30×0.35)/(2×0.12) ×(1/√2)=0.39G=Earth's magnetic field.
⟹ (μ0nI/2r) cos45o=(4π×10−7×30×0.35)/(2×0.12) ×(1/√2)=0.39G=Earth's magnetic field.
When iron filings are sprinkled on a sheet of glass placed over a short bar magnet then,- a)The iron filings form a pattern of suggesting that the magnet has north pole similar to the positive charge
- b)The iron filings form a random pattern of suggesting that the magnet has random pole
- c)The iron filings form a pattern suggesting that the magnet has two poles similar to the positive and negative charge of an electric dipole
- d)The iron filings form a pattern of suggesting that the magnet has south pole similar to the negative charge
Correct answer is option 'C'. Can you explain this answer?
When iron filings are sprinkled on a sheet of glass placed over a short bar magnet then,
a)
The iron filings form a pattern of suggesting that the magnet has north pole similar to the positive charge
b)
The iron filings form a random pattern of suggesting that the magnet has random pole
c)
The iron filings form a pattern suggesting that the magnet has two poles similar to the positive and negative charge of an electric dipole
d)
The iron filings form a pattern of suggesting that the magnet has south pole similar to the negative charge
|
Anjana Sen answered |
Explanation:North pole act as positive end and South pole act as negative end. The iron fillings in the presence of magnetic field gets magnetized and form a tiny magnet which then gets attracted to the poles of bar magnet. North pole of bar magnet attracts south pole of tiny magnet and vice-versa. So all the iron fillings are arranged as the magnetic field lines of bar magnet.
In Ferromagnetic materials- a)atomic magnetic moments are random in strong external fields
- b)strong interactions between atomic magnetic moments cause them to line up anti parallel to each other in external field
- c)weak interactions between atomic magnetic moments cause them to line up anti parallel to each other in external field
- d)strong interactions between atomic magnetic moments cause them to line up parallel to each other in regions called magnetic domains even if there is no external field
Correct answer is option 'D'. Can you explain this answer?
In Ferromagnetic materials
a)
atomic magnetic moments are random in strong external fields
b)
strong interactions between atomic magnetic moments cause them to line up anti parallel to each other in external field
c)
weak interactions between atomic magnetic moments cause them to line up anti parallel to each other in external field
d)
strong interactions between atomic magnetic moments cause them to line up parallel to each other in regions called magnetic domains even if there is no external field
|
Rajesh Chauhan answered |
A ferromagnetic substance contains permanent atomic magnetic dipoles that are spontaneously oriented parallel to one another even in the absence of an external field. The magnetic repulsion between two dipoles aligned side by side with their moments in the same direction makes it difficult to understand the phenomenon of ferromagnetism. It is known that within a ferromagnetic material, there is a spontaneous alignment of atoms in large clusters. A new type of interaction, a quantum mechanical effect known as the exchange interaction, is involved. A highly simplified description of how the exchange interaction aligns electrons in ferromagnetic materials is given here.
Diamagnetic substances are- a)those which have tendency to move from stronger to the weaker part of the external magnetic field
- b)those that are uneffected by external magnetic fields
- c)those that develop a net magnetic moment in direction of applied field
- d)those which have tendency to move from weaker to the stronger part of the external magnetic field
Correct answer is option 'A'. Can you explain this answer?
Diamagnetic substances are
a)
those which have tendency to move from stronger to the weaker part of the external magnetic field
b)
those that are uneffected by external magnetic fields
c)
those that develop a net magnetic moment in direction of applied field
d)
those which have tendency to move from weaker to the stronger part of the external magnetic field
|
|
Nabanita Sen answered |
When a diamagnetic material is placed in an external magnetic field the spin motion of electrons is so modified that the electrons which produce the moments in the direction of the external field show down while the electrons which produce magnetic moments in opposite directions get accelerated.
Thus, a net magnetic moment is induced in the opposite direction of the applied magnetic field. Hence the substance is magnetized opposite of the external field. Thus, it moves from stronger. Weaker parts of the magnetic.
Thus, a net magnetic moment is induced in the opposite direction of the applied magnetic field. Hence the substance is magnetized opposite of the external field. Thus, it moves from stronger. Weaker parts of the magnetic.
A bar magnet of magnetic moment 1.5 J/T lies aligned with the direction of a uniform magnetic field of 0.22 T. What is the amount of work required by an external torque to turn the magnet so as to align its magnetic moment opposite to the field direction?- a)0.66J
- b)0.76J nC
- c)0.86J
- d)0.56J
Correct answer is option 'A'. Can you explain this answer?
A bar magnet of magnetic moment 1.5 J/T lies aligned with the direction of a uniform magnetic field of 0.22 T. What is the amount of work required by an external torque to turn the magnet so as to align its magnetic moment opposite to the field direction?
a)
0.66J
b)
0.76J nC
c)
0.86J
d)
0.56J
|
Amar Choudhary answered |
Magnetic moment, M= 1.5 J T-1
Magnetic field strength, B= 0.22 T
W = - MB (cos θ2 - cos θ1)
= -1.5 x 0.22 (cos 180° - cos 0°)
= -0.33 (-1 - 1)
= 0.66 J
= -1.5 x 0.22 (cos 180° - cos 0°)
= -0.33 (-1 - 1)
= 0.66 J
The normal at any point q to the curve x = a (cos q + q sin q), y = a (sin q – q cos q) is at distance from the origin that is equal to… .- a)a
- b)2a
- c)4a
- d)3a
Correct answer is option 'A'. Can you explain this answer?
The normal at any point q to the curve x = a (cos q + q sin q), y = a (sin q – q cos q) is at distance from the origin that is equal to… .
a)
a
b)
2a
c)
4a
d)
3a
|
Athul Yadav answered |
Clearly, dx/dy =tan q = slope of normal = −cotq
Equation of normal at θ' is y−a(sinq − qcosq) = −cotq(x−a(cosq + qsinq)
= ysinq − asin2q + aqcosqsinq
= −xcosq + acos2q + aqsinqcosq
= xcosq + ysinq = a
Equation of normal at θ' is y−a(sinq − qcosq) = −cotq(x−a(cosq + qsinq)
= ysinq − asin2q + aqcosqsinq
= −xcosq + acos2q + aqsinqcosq
= xcosq + ysinq = a
permeability of a paramagnetic material is expected to decrease with increasing temperature because- a)random thermal motion increases magnetic moment alignment
- b)electrons stop moving
- c)electrons go into forbidden gap
- d)random thermal motion reduces magnetic moment alignment
Correct answer is option 'D'. Can you explain this answer?
permeability of a paramagnetic material is expected to decrease with increasing temperature because
a)
random thermal motion increases magnetic moment alignment
b)
electrons stop moving
c)
electrons go into forbidden gap
d)
random thermal motion reduces magnetic moment alignment
|
|
Rajdeep Sengupta answered |
When a parametric material comes close to a magnetic field the atoms will align with the magnetic field which causes another magnetic field. Permeability is the total magnetic field divided by the original magnetic field. Increase in temperature makes it harder for the atoms to align which decreases the strength of the second field. This results in a lower total magnetic field (numerator) and thus lower permeability.
which of the following features of atomic structure determine whether an element is diamagnetic or paramagnetic- a)orbital angular momentum ,spin angular momentum
- b)atomic weight
- c)number of electrons
- d)principal quantum number
Correct answer is option 'A'. Can you explain this answer?
which of the following features of atomic structure determine whether an element is diamagnetic or paramagnetic
a)
orbital angular momentum ,spin angular momentum
b)
atomic weight
c)
number of electrons
d)
principal quantum number
|
|
Shubham Jain answered |
Atomic Structure and Diamagnetism/Paramagnetism
Diamagnetism and paramagnetism are the two types of magnetism that an element can exhibit. Diamagnetic elements are those that have all their electrons paired up and do not have any unpaired electrons. Paramagnetic elements, on the other hand, have one or more unpaired electrons and are attracted to a magnetic field.
The features of atomic structure that determine whether an element is diamagnetic or paramagnetic are as follows:
Orbital Angular Momentum and Spin Angular Momentum
The orbital angular momentum and spin angular momentum of an electron are two important properties of atomic structure that determine whether an element is diamagnetic or paramagnetic. These properties are related to the magnetic moment of an electron, which is a measure of the strength of its magnetic field.
Diamagnetic elements have all their electrons paired up, which means that their magnetic moments cancel out and they have no net magnetic moment. In contrast, paramagnetic elements have one or more unpaired electrons, which means that they have a net magnetic moment and are attracted to a magnetic field.
Atomic Weight
The atomic weight of an element is the average weight of all the isotopes of that element. This property does not directly determine whether an element is diamagnetic or paramagnetic, but it can indirectly affect the magnetic properties of an element. Heavier elements tend to have more unpaired electrons, which makes them more likely to be paramagnetic.
Number of Electrons
The number of electrons in an atom is another important feature of atomic structure that determines whether an element is diamagnetic or paramagnetic. Elements with an odd number of electrons are more likely to be paramagnetic because they have at least one unpaired electron. Elements with an even number of electrons can be either diamagnetic or paramagnetic, depending on whether their electrons are paired or unpaired.
Principal Quantum Number
The principal quantum number of an electron is a measure of its energy level. This property does not directly determine whether an element is diamagnetic or paramagnetic, but it can indirectly affect the magnetic properties of an element. Electrons with higher energy levels are more likely to be unpaired, which makes them more likely to be paramagnetic.
Conclusion
In summary, the orbital angular momentum and spin angular momentum of an electron are the features of atomic structure that determine whether an element is diamagnetic or paramagnetic. Other features, such as atomic weight, number of electrons, and principal quantum number, can indirectly affect the magnetic properties of an element.
Diamagnetism and paramagnetism are the two types of magnetism that an element can exhibit. Diamagnetic elements are those that have all their electrons paired up and do not have any unpaired electrons. Paramagnetic elements, on the other hand, have one or more unpaired electrons and are attracted to a magnetic field.
The features of atomic structure that determine whether an element is diamagnetic or paramagnetic are as follows:
Orbital Angular Momentum and Spin Angular Momentum
The orbital angular momentum and spin angular momentum of an electron are two important properties of atomic structure that determine whether an element is diamagnetic or paramagnetic. These properties are related to the magnetic moment of an electron, which is a measure of the strength of its magnetic field.
Diamagnetic elements have all their electrons paired up, which means that their magnetic moments cancel out and they have no net magnetic moment. In contrast, paramagnetic elements have one or more unpaired electrons, which means that they have a net magnetic moment and are attracted to a magnetic field.
Atomic Weight
The atomic weight of an element is the average weight of all the isotopes of that element. This property does not directly determine whether an element is diamagnetic or paramagnetic, but it can indirectly affect the magnetic properties of an element. Heavier elements tend to have more unpaired electrons, which makes them more likely to be paramagnetic.
Number of Electrons
The number of electrons in an atom is another important feature of atomic structure that determines whether an element is diamagnetic or paramagnetic. Elements with an odd number of electrons are more likely to be paramagnetic because they have at least one unpaired electron. Elements with an even number of electrons can be either diamagnetic or paramagnetic, depending on whether their electrons are paired or unpaired.
Principal Quantum Number
The principal quantum number of an electron is a measure of its energy level. This property does not directly determine whether an element is diamagnetic or paramagnetic, but it can indirectly affect the magnetic properties of an element. Electrons with higher energy levels are more likely to be unpaired, which makes them more likely to be paramagnetic.
Conclusion
In summary, the orbital angular momentum and spin angular momentum of an electron are the features of atomic structure that determine whether an element is diamagnetic or paramagnetic. Other features, such as atomic weight, number of electrons, and principal quantum number, can indirectly affect the magnetic properties of an element.
Magnetic material differences are explained by- a)atoms contain moving electrons, and these electrons form microscopic current loops that produce magnetic fields of their own.
- b)number of neutrons
- c)number of protonsatoms contain spinning electrons, and their spin forms microscopic current loops that produce magnetic
- d)fields
Correct answer is option 'A'. Can you explain this answer?
Magnetic material differences are explained by
a)
atoms contain moving electrons, and these electrons form microscopic current loops that produce magnetic fields of their own.
b)
number of neutrons
c)
number of protonsatoms contain spinning electrons, and their spin forms microscopic current loops that produce magnetic
d)
fields
|
|
Gayatri Sharma answered |
All substances show some kind of magnetic behaviour. After all, they are made up of charged particles: electrons and protons. It is the way in which electron clouds arrange themselves in atoms and how groups of these atoms behave that determines the magnetic properties of the material. The atom (or group of atoms) in effect becomes a magnetic dipole or a mini bar magnet that can align according to the magnetic field applied. The net effect of all these dipoles determines the magnetic properties of the Magnetic Materials.
The equation of tangent to the curve y = x3 + 2x + 6 which is perpendicular to the line x + 14y + 4 = 0 is :- a)14x- y + 18 = 0
- b)14x -y + 1= 0
- c)14x- y + 22 = 0
- d)14x – y + 5 = 0
Correct answer is option 'C'. Can you explain this answer?
The equation of tangent to the curve y = x3 + 2x + 6 which is perpendicular to the line x + 14y + 4 = 0 is :
a)
14x- y + 18 = 0
b)
14x -y + 1= 0
c)
14x- y + 22 = 0
d)
14x – y + 5 = 0
|
|
Samridhi Desai answered |
y = x3 + 2x + 6
Slope of tangent = m1 = dy/dx = 3x3 + 2
Slope of perpendicular line = m2 = −1/14
m1 . m2 = -1
m1 = 14
3x2 + 2 = 14
x = ±2
Therefore the curve has tangents at x = 2 and x = -2
and these points also lie on the given curve
Equation of tangent - y = 14x + c
Coordinates of points of tangency
At x = 2 , y = 23 + 2(2) + 6 = 18
At x = -2 , y = (-2)3 + 2(-2) + 6 = -6
18 = 14(2) + c
c = -10
-6 = 14(-2) + c
c = 22
Equation of tangent - y = 14x - 10 and y = 14x + 22
Hence, 14x - y +22 = 0
Slope of tangent = m1 = dy/dx = 3x3 + 2
Slope of perpendicular line = m2 = −1/14
m1 . m2 = -1
m1 = 14
3x2 + 2 = 14
x = ±2
Therefore the curve has tangents at x = 2 and x = -2
and these points also lie on the given curve
Equation of tangent - y = 14x + c
Coordinates of points of tangency
At x = 2 , y = 23 + 2(2) + 6 = 18
At x = -2 , y = (-2)3 + 2(-2) + 6 = -6
18 = 14(2) + c
c = -10
-6 = 14(-2) + c
c = 22
Equation of tangent - y = 14x - 10 and y = 14x + 22
Hence, 14x - y +22 = 0
The equations of the tangents drawn to the curve y2 – 2x3 – 4y + 8 = 0 from the point (1, 2) is… .- a)
- b)
- c)
- d)
Correct answer is option 'D'. Can you explain this answer?
The equations of the tangents drawn to the curve y2 – 2x3 – 4y + 8 = 0 from the point (1, 2) is… .
a)
b)
c)
d)
|
|
Rajesh Chauhan answered |
Let P(α, β) be any point on the curve
Now, the equation of the tangent at P is
Hence, the point of contacts are
(2, 2 + 2√3) and (2, 2 – 2√3)
Slope of the tangents are 2√3 , –2√3
Hence, the equations of tangents are
y – (2 + 2√3) = 2√3 (x – 2)
and
y –(2 – 2√3) = – 2√3 (x – 2)
Now, the equation of the tangent at P is
Hence, the point of contacts are
(2, 2 + 2√3) and (2, 2 – 2√3)
Slope of the tangents are 2√3 , –2√3
Hence, the equations of tangents are
y – (2 + 2√3) = 2√3 (x – 2)
and
y –(2 – 2√3) = – 2√3 (x – 2)
Which of the following statements about bar magnets is correct ?- a)We can isolate the north and south pole of a bar magnet.
- b)North Pole atrracts North Pole.
- c)South Pole atrracts South Pole.
- d)We cannot isolate the north and south pole of a bar magnet.
Correct answer is option 'D'. Can you explain this answer?
Which of the following statements about bar magnets is correct ?
a)
We can isolate the north and south pole of a bar magnet.
b)
North Pole atrracts North Pole.
c)
South Pole atrracts South Pole.
d)
We cannot isolate the north and south pole of a bar magnet.
|
Srestha Choudhury answered |
Explanation:As magnetic monopole does not exist. If we split the bar magnet into two pieces each part will have its own north and south pole.
Far axial magnetic field of a solenoid as well as bar magnet vary- a)directly as R squared R = axial distance to the magnet/solenoid
- b)inversely as R squared R = axial distance to the magnet/solenoid
- c)directly as R cubed R = axial distance to the magnet/solenoid
- d)inversely as R cubed R = axial distance to the magnet/solenoid
Correct answer is option 'D'. Can you explain this answer?
Far axial magnetic field of a solenoid as well as bar magnet vary
a)
directly as R squared R = axial distance to the magnet/solenoid
b)
inversely as R squared R = axial distance to the magnet/solenoid
c)
directly as R cubed R = axial distance to the magnet/solenoid
d)
inversely as R cubed R = axial distance to the magnet/solenoid
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Tanvi Bose answered |
For a short Bar Magnet, the magnetic induction at a point on the axis at a distance r from centre is given by the formula
B= (μ0/4π) (2M/r3)
⇒ B= K/ r3
⇒ B∝1/r3
The correct answer is option D.
B= (μ0/4π) (2M/r3)
⇒ B= K/ r3
⇒ B∝1/r3
The correct answer is option D.
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