Advanced countries are making use of powerful electromagnets to move trains at very high speed. These trains are called maglev trains (abbreviated from magnetic levitation). These trains float on a guideway and do not run on steel rail tracks.Instead of using a engine based on fossil fuels, they make use of magnetic field forces. The magnetized coils are arranged in the guide way which repels the strong magnets placed in the train's under carriage. This helps train move over the guideway , a technic called electrodynamic suspension. When current passes in the coils of guideway , a typical magnetic field is set up between the undercarriage of train and guideway which pushes and pull the train along the guideway depending on the requirement.The lack of friction and its aerodynamic style allows the train to more at very high speed.
Q.1. The levitation of the train is due to
The magnetised coils running along the track repel large magnets on the train's under carriage.
Advanced countries are making use of powerful electromagnets to move trains at very high speed. These trains are called maglev trains (abbreviated from magnetic levitation). These trains float on a guideway and do not run on steel rail tracks.Instead of using a engine based on fossil fuels, they make use of magnetic field forces. The magnetized coils are arranged in the guide way which repels the strong magnets placed in the train's under carriage. This helps train move over the guideway , a technic called electrodynamic suspension. When current passes in the coils of guideway , a typical magnetic field is set up between the undercarriage of train and guideway which pushes and pull the train along the guideway depending on the requirement.The lack of friction and its aerodynamic style allows the train to more at very high speed.
Q.2. The disadvantage of maglev trains is that
Initial cost will be more.
Advanced countries are making use of powerful electromagnets to move trains at very high speed. These trains are called maglev trains (abbreviated from magnetic levitation). These trains float on a guideway and do not run on steel rail tracks.Instead of using a engine based on fossil fuels, they make use of magnetic field forces. The magnetized coils are arranged in the guide way which repels the strong magnets placed in the train's under carriage. This helps train move over the guideway , a technic called electrodynamic suspension. When current passes in the coils of guideway , a typical magnetic field is set up between the undercarriage of train and guideway which pushes and pull the train along the guideway depending on the requirement.The lack of friction and its aerodynamic style allows the train to more at very high speed.
Q.3. The force which makes maglev move
The magnetic force will pull the vehicle.
The figure shows a circular loop of radius a with two long parallel wires (numbered 1 and 2) all in the plane of the paper. The distance of each wire from the centre of the loop is d. The loop and the wire are carrying the same current I.The current in the loop is in the counterclockwise direction if seen from above.
(q) The magnetic fields (B) at P due to the currents in the wires are in opposite directions.
(r) There is no magnetic field at P.
(s) The wires repel each other.
Q.4.When d ≈ a but wires are not touching the loop, it is found that the net magnetic field on the axis of the loop is zero at a height h above the loop. In that case
Magnetic field due to current carrying loop = Magnetic field due to straight wires
B = B_{1}cos θ + B_{2}cos θ = 2 B_{1}cos θ
The current is from P to Q in wire 1 and from R to S in wire 2.
The figure shows a circular loop of radius a with two long parallel wires (numbered 1 and 2) all in the plane of the paper. The distance of each wire from the centre of the loop is d. The loop and the wire are carrying the same current I.The current in the loop is in the counterclockwise direction if seen from above.
(q) The magnetic fields (B) at P due to the currents in the wires are in opposite directions.
(r) There is no magnetic field at P.
(s) The wires repel each other.
Q.5. Consider d >> a, and the loop is rotated about its diameter parallel to the wires by 30° from the position shown in the figure. If the currents in the wires are in the opposite directions, the torque on the loop at its new position will be (assume that the net field due to the wires is constant over the loop).
We know that torque
In a thin rectangular metallic strip a constant current I flows along the positive xdirection, as shown in the figure. The length, width and thickness of the strip are l, w and d, respectively.A uniform magnetic field is applied on the strip along the positive ydirection. Due to this, the charge carriers experience a net deflection along the zdirection. This results in accumulation of charge carriers on the surface PQRS and appearance of equal and opposite charges on the face opposite to PQRS. A potential difference along the zdirection is thus developed. Charge accumulation continues until the magnetic force is balanced by the electric force. The current is assumed to be uniformly distributed on the crosssection of the strip and carried by electrons.
Q.6. Consider two different metallic strips (1 and 2) of the same material. Their lengths are the same, widths are w_{1} and w_{2} and thicknesses are d_{1} and d_{2} respectively. Two points K and M are symmetrically located on the opposite faces parallel to the xy plane (see figure). V_{1} and V_{2} are the potential differences between K and M in strips 1 and 2, respectively. Then, for a given current I flowing through them in a given magnetic field strength B, the correct statement(s) is(are)
When megnetic force balances electric force F_{B} = F_{E}
q v_{d} B = q _{E}
_{}
_{ }
_{}
when d_{1} = 2d_{2}, V_{2} = 2V_{1}
and when d_{1} = d_{2}, V_{2} = V_{1} (a), (d) are correct options
In a thin rectangular metallic strip a constant current I flows along the positive xdirection, as shown in the figure. The length, width and thickness of the strip are l, w and d, respectively.A uniform magnetic field is applied on the strip along the positive ydirection. Due to this, the charge carriers experience a net deflection along the zdirection. This results in accumulation of charge carriers on the surface PQRS and appearance of equal and opposite charges on the face opposite to PQRS. A potential difference along the zdirection is thus developed. Charge accumulation continues until the magnetic force is balanced by the electric force. The current is assumed to be uniformly distributed on the crosssection of the strip and carried by electrons.
Q.7. Consider two different metallic strips (1 and 2) of same dimensions (length l, width w and thickness d) with carrier densities n_{1} and n_{2}, respectively. Strip 1 is placed in magnetic field B_{1} and strip 2 is placed in magnetic field B_{2}, both along positive ydirections. Then V_{1} and V_{2} are the potential differences developed between K and M in strips 1 and 2, respectively. Assuming that the current I is the same for both the strips, the correct option(s) is(are)
Here
A and C are the correct options.
Statement1 : The sensitivity of a moving coil galvanometer is increased by placing a suitable magnetic material as a core inside the coil. and Statement2 : Soft iron has a high magnetic permeability and cannot be easily magnetized or demagnetized.
Statemen t1 is tr ue. Sensitivity =. If B increases, θ/I
increases. Statement2 is wrong because soft iron can be easily magnetised and de magnetized.
If in a circular coil A of radius R, current I is flowing and in another coil B of radius 2R a current 2I is flowing, then the ratio of the magnetic fields B_{A} and B_{B}, produced by them will be
KEY CONCEPT : We know that the magnetic field produced by a current carrying circular coil of radius r at its centre is
If an electron and a proton having same momenta enter perpendicular to a magnetic field, then
KEY CONCEPT : When a charged particle enters perpendicular to a magnetic field, then it moves in a circular path of radius.
where q = Charge of the particle
p = Momentum of the particle
B = Magnetic field
Here p, q and B are constant for electron and proton, therefore the radius will be same.
Wires 1 and 2 carrying currents i_{1} and i_{2} respectively are inclined at an angle θ to each other. What is the force on a small element dl of wire 2 at a distance of r from wire 1 (as shown in figure) due to the magnetic field of wire 1?
Magnetic field due to current in wire 1 at point P distant r from the wire is
(directed perpendicular to the plane of paper, inwards)
The force exerted due to this magnetic field on current element i_{2} dl is
dF = i_{2 }dl B sin 90°
The time period of a charged particle undergoing a circular motion in a uniform magnetic field is independent of its
KEY CONCEPT : The time period of a charged particle (m, q) moving in a magnetic field (B) is T= 2πm/qB
The time period does not depend on the speed of the particle.
A particle of mass M and charge Q moving with velocity describe a circular path of radius R when subjected to a uniform transverse magnetic field of induction B. The work done by the field when the particle completes one full circle is
The workdone, dW = Fds cosθ The angle between force and displacement is 90° .
Therefore work done is zero.
A particle of charge  16 *10 ^{18 }coulomb moving with velocity 10ms^{1} along the xaxis enters a region where a magnetic field of induction B is along the yaxis, and an electric field of magnitude 10^{ 4} V / m is along the negative zaxis. If the charged particle continues moving along the xaxis, the magnitude of B is
The situation is shown in the figure.
F_{E}= Force due to electric field F_{B} = Force due to magnetic field It is given that the charged particle remains moving along Xaxis (i.e. undeviated). Therefore F_{B} = F_{E}
A thin rectangular magnet suspended freely has a period of oscillation equal to T. Now it is broken into two equal halves (each having half of the original length) and one piece is made to oscillate freely in the same field. If its period of oscillation is T ' , the ratio T '/T is
KEY CONCEPT : The time period of a rectangular magnet oscillating in earth’s magnetic field is given by
where I = Moment of inertia of the rectangular magnetm
μ= Magnetic moment
B_{H} = Horizontal component of the earth’s magnetic field
Case 2 : Magnet is cut into two identical pieces such that each piece has half the original length. Then
A magnetic needle lying parallel to a magnetic field requiers W units of work to turn it through 60^{0} . The torque needed to maintain the needle in this position will be
W = MB(cos θ_{1}  cosθ_{2} )
= MB(cos 0°  cos 60°)
The magnetic lines of force inside a bar magnet
As shown in the figure, the magnetic lines of force are directed from south to north inside a bar magnet.
Curie temperature is the temperature above which
KEY CONCEPT : The temperature above which a ferromagnetic substance becomes paramagnetic is called Curie’s temperature.
A current i ampere flows along an infinitely long straight thin walled tube, then the magnetic induction at any point inside the tube is
Using Ampere’s law at a distance r from axis, B is same from symmetry.
Here i is zero, for r < R, whereas R is the radius
∴B = 0
A long wire carries a steady current. It is bent into a circle of one turn and the magnetic field at the centre of the coil is B. It is then bent into a circular loop of n turns. The magnetic field at the centre of the coil will be
KEY CONCEPT : Magentic field at the centre of a circular coil of radius R carrying current i is
Given : n ´ (2pr ') =2pR
⇒ nr '=R ...(1)
from (1) and (2),
The magnetic field due to a current carrying circular loop of radius 3 cm at a point on the axis at a distance of 4 cm from the centre is 54 μT. What will be its value at the centre of loop?
The magnetic field at a point on the axis of a circular loop at a distance x from centre is,
Two long conductors, separated by a distance d carry current I_{1} and I_{2} in the same direction. They exert a force F on each other. Now the current in one of them is increased to two times and its direction is reversed. The distance is also increased to 3d. The new value of the force between them is
Force between two long conductor carrying current,
The length of a magnet is large compared to its width and breadth. The time period of its oscillation in a vibration magnetometer is 2s. The magnet is cut along its length into three equal parts and these parts are then placed on each other with their like poles together. The time period of this combination will be
When the magnet is cut into three pieces the pole strength will remain the same and
We have, Magnetic moment (M) = Pole strength (m) × l
∴ New magnetic moment,
The materials suitable for making electromagnets should have
NOTE : Electr o mag n et sh ould be amen abl e to magnetisation & demagnetization.
∴ retentivity should be low & coercivity should be low
Two concentric coils each of radius equal to 2 π cm are placed at right angles to each other. 3 ampere and 4 ampere are the currents flowing in each coil respectively. The magnetic induction in Weber / m^{2} at the centre of the coils will be
The magnetic field due to circular coil 1 and 2 are
A charged particle of mass m and charge q travels on a circular path of radius r that is perpendicular to a magnetic field B. The time taken by the particle to complete one revolution is
Equating magnetic force to centripetal force,
Time to complete one revolution,
A magnetic needle is kept in a nonuniform magnetic field. It experiences
A magnetic needle kept in non uniform magnetic field experience a force and torque due to unequal forces acting on poles.
A uniform electric field and a uniform magnetic field are acting along the same direction in a certain region. If an electron is projected along the direction of the fields with a certain velocity then
Due to electric field, it experiences force and decelerates i.e. its velocity decreases.
Needles N_{1}, N_{2} and N_{3} are made of a ferromagnetic, a paramagnetic and a diamagnetic substance respectively. A magnet when brought close to them will
Ferromagnetic substance has magnetic domains whereas paramagnetic substances have magnetic dipoles which get attracted to a magnetic field.
Diamagnetic substances do not have magnetic dipole but in the presence of external magnetic field due to their orbital motion of electrons these substances are repelled.
In a region, steady and uniform electric and magnetic fields are present. These two fields are parallel to each other. A charged particle is released from rest in this region. The path of the particle will be a
The charged particle will move along the lines of electric field (and magnetic field). Magnetic field will exert no force. The force by electric field will be along the lines of uniform electric field. Hence the particle will move in a straight line.
A long solenoid has 200 turns per cm and carries a current i. The magnetic field at its centre is 6.28 × 10^{–2} Weber/m^{2}. Another long solenoid has 100 turns per cm and it carries a current i/3 . The value of the magnetic field at its centre is
A long straight wire of radius a carries a steady current i. The current is uniformly distributed across its cross section. The ratio of the magnetic field at a/2 and 2a is
Here, current is uniformly distributed across the crosssection of the wire, therefore, current enclosed in the amperean path formed at a distance
where I is total current
∴ Magnetic field at P_{1} is
Now, magnetic field at point P_{2},
A current I flows along the length of an infinitely long, straight, thin walled pipe. Then
There is no current inside the pipe. Therefore
A charged particle with charge q enters a region of constant, uniform and mutually orthogonal fields with a velocity and comes out without any change in magnitude or direction .Then
Here, are perpendicular to each other and the velocity does not change; therefore
Also,
A charged particle moves through a magnetic field perpendicular to its direction. Then
NOTE : When a charged particle enters a magnetic field at a direction perpendicular to the direction of motion, the path of the motion is circular. In circular motion the direction of velocity changes at every point (the magnitude remains constant).
Therefore, the tangential momentum will change at every point. But kinetic energy will remain constant as it is given by
1/2 mv^{2} and v^{2} is the squar e of th e magnitude of velocity which does not change.
Two identical conducting wires AOB and COD are placed at right angles to each other. The wire AOB carries an electric current I_{1} and COD carries a current I_{2}. The magnetic field on a point lying at a distance d from O, in a direction perpendicular to the plane of the wires AOB and COD, will be given by
Clearly, the magnetic fields at a point P, equidistant from AOB and COD will have directions perpendicular to each other, as they are placed normal to each other.
A horizontal overhead powerline is at height of 4m from the ground and carries a current of 100A from east to west. The magnetic field directly below it on the ground is
The magnetic field is
= 5 × 10^{–6} T
According to right hand palm rule, the magnetic field is directed towards south.
Relative permittivity and permeability of a material ε_{r} and μ_{r} , respectively. Which of the following values of these quantities are allowed for a diamagnetic material?
For a diamagnetic material, the value of µ_{r} is less than one. For any material, the value of ∈_{r} is always greater than 1.
A current loop ABCD is held fixed on the plane of the paper as shown in the figure. The arcs BC (radius = b) and DA (radius = a) of the loop are joined by two straight wires AB and CD. A steady current I is flowing in the loop. Angle made by AB and CD at the origin O is 30°. Another straight thin wire with steady current I_{1} flowing out of the plane of the paper is kept at the origin.
Q.31. The magnitude of the magnetic field (B) due to the loop ABCD at the origin (O) is :
The magnetic field at O due to current in DA is
(directed vertically upwards)
The magnetic field at O due to current in BC is
(directed vertically downwards)
The magnetic field due to current AB and CD at O is zero.
Therefore the net magnetic field is B = B_{1}B_{2} (directed vertically upwards)
A current loop ABCD is held fixed on the plane of the paper as shown in the figure. The arcs BC (radius = b) and DA (radius = a) of the loop are joined by two straight wires AB and CD. A steady current I is flowing in the loop. Angle made by AB and CD at the origin O is 30°. Another straight thin wire with steady current I_{1} flowing out of the plane of the paper is kept at the origin.
Q.32.Due to the presence of the current I_{1 }at the origin:
The force on AD and BC due to current I1 is zero. This is because the directions of current element and magnetic field
Two long parallel wires are at a distance 2d apart. They carry steady equal currents flowing out of the plane of the paper as shown. The variation of the magnetic field B along the line XX' is given by
The magnetic field varies inversely with the distance for a long conductor. That is According to the magnitude and direction shown graph (1) is the correct one.
A current I flows in an infinitely long wire with cross section in the form of a semicircular ring of radius R. The magnitude of the magnetic induction along its axis is:
Current in a small element,
Magnetic field due to the element
The component dB cos θ, of the field is cancelled by another opposite component.
Therefore,
A charge Q is uniformly distributed over the surface of nonconducting disc of radius R. The disc rotates about an axis perpendicular to its plane and passing through its centre with an angular velocity ω. As a result of this rotation a magnetic field of induction B is obtained at the centre of the disc. If we keep both the amount of charge placed on the disc and its angular velocity to be constant and vary the radius of the disc then the variation of the magnetic induction at the centre of the disc will be represented by the figure :
The magnetic field due a disc is given as
Proton, deuteron and alpha particle of same kinetic energy are moving in circular trajectories in a constant magnetic field. The radii of proton, deuteron and alpha particle are respectively r_{p}, r_{d} and r_{α}. Which one of the following relation is correct?
Thus we have,
Two short bar magnets of length 1 cm each have magnetic moments 1.20 Am^{2} and 1.00 Am^{2} respectively. They are placed on a horizontal table parallel to each other with their N poles pointing towards the South. They have a common magnetic equator and are separated by a distance of 20.0 cm. The value of the resultand horizontal magnetic induction at the midpoint O of the line joining their centres is close to (Horizontal component of earth.s magnetic induction is 3.6× 10.5Wb/m^{2})
Given : 2 M_{1} = 1.20 Am^{2} and M_{2} = 1.00 Am^{2}
^{}
B_{net} = B_{1} + B_{2} + B_{H}
_{}
_{}
A conductor lies along the zaxis at and carries a fixed current of 10.0 A in direction (see figure).For a field T, find the power required to move the conductor at constant speed to x = 2.0 m, y = 0 m in 5*10^{3}s. Assume parallel motion along the xaxis.
Work done in moving the conductor is,
_{}
_{}
_{}
(By exponential function)
_{}
= 9 × 10^{–3} × (0.33) = 2.97 × 10^{–3}J
Power required to move the conductor is,
The coercivity of a small magnet where the ferromagnet gets demagnetized is 3*10^{3}Am^{1}. The current required to be passed in a solenoid of length 10 cm and number of turns 100, so that the magnet gets demagnetized when inside the solenoid, is:
Magnetic field in solenoid B =μ_{0}ni
(Where n = number of turns per unit length)
Two long current carrying thin wires, both with current I, are held by insulating threads of length L and are in equilibrium as shown in the figure, with threads making an angle 'θ' with the vertical. If wires have mass λ per unit length then the value of I is :
(g = gravitational acceleration)
Let us consider 'l' length of current carrying wire.
At equilibrium
A rectangular loop of sides 10 cm and 5 cm carrying a current 1 of 12 A is placed in different orientations as shown in the figures below :
(a)(b)
(c) (d)
If there is a uniform magnetic field of 0.3 T in the positive z direction, in which orientations the loop would be in (i) stable equilibrium and (ii) unstable equilibrium ?
For stable equilibrium
For unstable equilibrium
Two identical wires A and B, each of length 'l', carry the same current I. Wire A is bent into a circle of radius R and wire B is bent to form a square of side 'a'. If B_{A} and B_{B} are the values of magnetic field at the centres of the circle and square respectively, then the ratio
Case (b) :
A galvanometer having a coil resistance of 100 Ω gives a full scale deflection, when a currect of 1 mA is passed through it. The value of the resistance, which can convert this galvanometer into ammeter giving a full scale deflection for a current of 10 A, is :
Ig G = ( I – Ig)s
∴ 10^{–3} × 100 = (10 – 10^{–3}) × S
∴ S ≈ 0.01 Ω
Hysteresis loops for two magnetic materials A and B are given below :
These materials are used to make magnets for elecric generators, transformer core and electromagnet core. Then it is proper to use :
Graph [A] is for material used for making permanent magnets (high coercivity)
Graph [B] is for making electromagnets and transformers.
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