DC Pandey Solutions: Magnetics | Physics Class 12 - NEET PDF Download

 Page 1


Introductory Exercise 23.1
Q.1. Write the dimensions of E/B. Here, E is the electric field and B the
magnetic field.  
Sol. qE = Bqv sin ?
[E/B] = [v] = [LT ]
Q.2. In the relation which pairs are always perpendicular to
each other.
Sol. From the property of cross product  is always perpendicular to both 
Q.3. If a beam o f electrons travels in a straight line in a certain region. Can
we say there is no magnet ic field?
Sol.  both may be present and may be possible that, 
Q.4. A charge q = -4µC has an instantaneous velocity  
 in a uniform magnetic field 
 What is the force on the charge?
Sol.
Here, q has to be substituted with sign.
Introductory Exercise 23.2
-1
Page 2


Introductory Exercise 23.1
Q.1. Write the dimensions of E/B. Here, E is the electric field and B the
magnetic field.  
Sol. qE = Bqv sin ?
[E/B] = [v] = [LT ]
Q.2. In the relation which pairs are always perpendicular to
each other.
Sol. From the property of cross product  is always perpendicular to both 
Q.3. If a beam o f electrons travels in a straight line in a certain region. Can
we say there is no magnet ic field?
Sol.  both may be present and may be possible that, 
Q.4. A charge q = -4µC has an instantaneous velocity  
 in a uniform magnetic field 
 What is the force on the charge?
Sol.
Here, q has to be substituted with sign.
Introductory Exercise 23.2
-1
Q.1. Can a charged particle be accelerated by a magnetic field. Can its
speed be increased?
Sol Magnetic force may be non-zero. Hence acceleration due to magnetic force may
be non-zero. Magnetic force is always perpendicular to velocity. Hence its power is
always zero or work done by magnetic force is always zero. Hence it can be change
the speed of charged particle.
Q.2. An electron beam projected along positive x-axis deflects along the
positive y-axis. If this deflection is caused by a magnetic field, what is the
direction of the field?
Sol: 
 is along position y -direction, q is negative and  is along positive x-direction.
Therefore  should be along positive z-direction.
Q.3. An electron and a proton are projected with same velocity
perpendicular to a magnetic field,
(a) Which particle will describe the smaller circle?
(b) Which particle will have greater frequency?
Sol.  as other factors are same.
Q.4. In a region of space a uniform magnetic field 6 is along positive x-axis.
Electrons are emitted from the origin with speed v at different angles. Show
that the paraxial electrons are refocused on the x-axis at a distance 
 Here, m is the mass of electron and e the charge on it.
Sol. 
Electrons touches the x-axis again after every pitch. Therefore the asked distance is
d = p = v T
11
Page 3


Introductory Exercise 23.1
Q.1. Write the dimensions of E/B. Here, E is the electric field and B the
magnetic field.  
Sol. qE = Bqv sin ?
[E/B] = [v] = [LT ]
Q.2. In the relation which pairs are always perpendicular to
each other.
Sol. From the property of cross product  is always perpendicular to both 
Q.3. If a beam o f electrons travels in a straight line in a certain region. Can
we say there is no magnet ic field?
Sol.  both may be present and may be possible that, 
Q.4. A charge q = -4µC has an instantaneous velocity  
 in a uniform magnetic field 
 What is the force on the charge?
Sol.
Here, q has to be substituted with sign.
Introductory Exercise 23.2
-1
Q.1. Can a charged particle be accelerated by a magnetic field. Can its
speed be increased?
Sol Magnetic force may be non-zero. Hence acceleration due to magnetic force may
be non-zero. Magnetic force is always perpendicular to velocity. Hence its power is
always zero or work done by magnetic force is always zero. Hence it can be change
the speed of charged particle.
Q.2. An electron beam projected along positive x-axis deflects along the
positive y-axis. If this deflection is caused by a magnetic field, what is the
direction of the field?
Sol: 
 is along position y -direction, q is negative and  is along positive x-direction.
Therefore  should be along positive z-direction.
Q.3. An electron and a proton are projected with same velocity
perpendicular to a magnetic field,
(a) Which particle will describe the smaller circle?
(b) Which particle will have greater frequency?
Sol.  as other factors are same.
Q.4. In a region of space a uniform magnetic field 6 is along positive x-axis.
Electrons are emitted from the origin with speed v at different angles. Show
that the paraxial electrons are refocused on the x-axis at a distance 
 Here, m is the mass of electron and e the charge on it.
Sol. 
Electrons touches the x-axis again after every pitch. Therefore the asked distance is
d = p = v T
11
For paraxial electrons ? ˜ 0° and q = e
?  
Q.5. A particle of mass m and charge q is projected into a region having a
perpendicular magnetic field 6. Find the angle of deviation of the particle as
it comes out of the magnetic field if the width of the region is,
 
Sol.
and ? = p if L = r
Q.6. An electron is accelerated through a PD of 100 V and then enters a
region where it is moving perpendicular to a magnetic field S = 0.2 T. Find
the radius of the circular path. Repeat this problem for a proton.
Sol. 
Q.7. A proton, a deutron and an a-particle have equal kinetic energies.
Compare the radii of their paths when a normal magnetic field is applied.
Page 4


Introductory Exercise 23.1
Q.1. Write the dimensions of E/B. Here, E is the electric field and B the
magnetic field.  
Sol. qE = Bqv sin ?
[E/B] = [v] = [LT ]
Q.2. In the relation which pairs are always perpendicular to
each other.
Sol. From the property of cross product  is always perpendicular to both 
Q.3. If a beam o f electrons travels in a straight line in a certain region. Can
we say there is no magnet ic field?
Sol.  both may be present and may be possible that, 
Q.4. A charge q = -4µC has an instantaneous velocity  
 in a uniform magnetic field 
 What is the force on the charge?
Sol.
Here, q has to be substituted with sign.
Introductory Exercise 23.2
-1
Q.1. Can a charged particle be accelerated by a magnetic field. Can its
speed be increased?
Sol Magnetic force may be non-zero. Hence acceleration due to magnetic force may
be non-zero. Magnetic force is always perpendicular to velocity. Hence its power is
always zero or work done by magnetic force is always zero. Hence it can be change
the speed of charged particle.
Q.2. An electron beam projected along positive x-axis deflects along the
positive y-axis. If this deflection is caused by a magnetic field, what is the
direction of the field?
Sol: 
 is along position y -direction, q is negative and  is along positive x-direction.
Therefore  should be along positive z-direction.
Q.3. An electron and a proton are projected with same velocity
perpendicular to a magnetic field,
(a) Which particle will describe the smaller circle?
(b) Which particle will have greater frequency?
Sol.  as other factors are same.
Q.4. In a region of space a uniform magnetic field 6 is along positive x-axis.
Electrons are emitted from the origin with speed v at different angles. Show
that the paraxial electrons are refocused on the x-axis at a distance 
 Here, m is the mass of electron and e the charge on it.
Sol. 
Electrons touches the x-axis again after every pitch. Therefore the asked distance is
d = p = v T
11
For paraxial electrons ? ˜ 0° and q = e
?  
Q.5. A particle of mass m and charge q is projected into a region having a
perpendicular magnetic field 6. Find the angle of deviation of the particle as
it comes out of the magnetic field if the width of the region is,
 
Sol.
and ? = p if L = r
Q.6. An electron is accelerated through a PD of 100 V and then enters a
region where it is moving perpendicular to a magnetic field S = 0.2 T. Find
the radius of the circular path. Repeat this problem for a proton.
Sol. 
Q.7. A proton, a deutron and an a-particle have equal kinetic energies.
Compare the radii of their paths when a normal magnetic field is applied.
Sol. 
Page 5


Introductory Exercise 23.1
Q.1. Write the dimensions of E/B. Here, E is the electric field and B the
magnetic field.  
Sol. qE = Bqv sin ?
[E/B] = [v] = [LT ]
Q.2. In the relation which pairs are always perpendicular to
each other.
Sol. From the property of cross product  is always perpendicular to both 
Q.3. If a beam o f electrons travels in a straight line in a certain region. Can
we say there is no magnet ic field?
Sol.  both may be present and may be possible that, 
Q.4. A charge q = -4µC has an instantaneous velocity  
 in a uniform magnetic field 
 What is the force on the charge?
Sol.
Here, q has to be substituted with sign.
Introductory Exercise 23.2
-1
Q.1. Can a charged particle be accelerated by a magnetic field. Can its
speed be increased?
Sol Magnetic force may be non-zero. Hence acceleration due to magnetic force may
be non-zero. Magnetic force is always perpendicular to velocity. Hence its power is
always zero or work done by magnetic force is always zero. Hence it can be change
the speed of charged particle.
Q.2. An electron beam projected along positive x-axis deflects along the
positive y-axis. If this deflection is caused by a magnetic field, what is the
direction of the field?
Sol: 
 is along position y -direction, q is negative and  is along positive x-direction.
Therefore  should be along positive z-direction.
Q.3. An electron and a proton are projected with same velocity
perpendicular to a magnetic field,
(a) Which particle will describe the smaller circle?
(b) Which particle will have greater frequency?
Sol.  as other factors are same.
Q.4. In a region of space a uniform magnetic field 6 is along positive x-axis.
Electrons are emitted from the origin with speed v at different angles. Show
that the paraxial electrons are refocused on the x-axis at a distance 
 Here, m is the mass of electron and e the charge on it.
Sol. 
Electrons touches the x-axis again after every pitch. Therefore the asked distance is
d = p = v T
11
For paraxial electrons ? ˜ 0° and q = e
?  
Q.5. A particle of mass m and charge q is projected into a region having a
perpendicular magnetic field 6. Find the angle of deviation of the particle as
it comes out of the magnetic field if the width of the region is,
 
Sol.
and ? = p if L = r
Q.6. An electron is accelerated through a PD of 100 V and then enters a
region where it is moving perpendicular to a magnetic field S = 0.2 T. Find
the radius of the circular path. Repeat this problem for a proton.
Sol. 
Q.7. A proton, a deutron and an a-particle have equal kinetic energies.
Compare the radii of their paths when a normal magnetic field is applied.
Sol. 
Introductory Exercise 23.3 
Q 1.  In a certain region uniform electric field 
0
ˆ
E E k ??
?
and magnetic field 
0
ˆ
B B k ??
?
are present. At 
time t = 0 a particle of mass m and charge q is given a velocity 
00
ˆˆ
v v j v k ??
?
.
 
Find the minimum 
speed of the particle and the time when it happens so. 
 
Q 2.  A particle of mass m and charge q is lying at the origin in a uniform magnetic field B directed 
along x-axis. At time t = 0, it is given a velocity v
0
 at an angle ? with the y-axis in the xy-plane. 
Find the coordinates of the particle after one revolution. 
Q 3.  A wire of length l carries a current i along the x-axis. A magnetic field 
0
ˆˆ
B B (j k) ??
?
exists in the 
space. Find the magnitude of the magnetic force acting on the wire. 
Q 4.  In the above problem will the answer change if magnetic field becomes 
   
0
ˆ ˆ ˆ
B B (i j k) ? ? ?
?
 
Solutions 
1.  (along negative z-direction) 
Electric field will make z-component of velocity zero. At that time speed of the particle will be 
minimum and that minimum speed is the other component i. e., v
0
. This is minimum when, 
   
2.  Path is helix and after one rotation only x-coordinate will change by a distance equal to pitch. 
   
3.  
   
4.  No it will not change, as the new component of is in the direction of 
Introductory Exercise 23.4 
Q 1.  A charge q is uniformly distributed on a nonconducting disc of radius Ft. It is rotated with an 
angular speed a about an axis passing through the centre of mass of the disc and perpendicular to 
its plane. Find the magnetic moment of the disc. 
  [Hint: Magnetic moment = 
q
2m
??
??
??
(angular momentum)] 
Q 2.  Find the magnetic moment of the current carrying loop OABCO shown in figure. 
  Given that, i = 4.0 A, OA = 20 cm and AB =10 cm.