DC Pandey Solutions (JEE Main): Magnetics | DC Pandey Solutions for JEE Physics PDF Download

 Page 1


Exercises 
For JEE Main 
  Subjective Questions 
  Note You can take approximations in the answers. 
  Magnetic Force on a Charged Particle in Motion 
Q 1.  A particle initially moving towards south in a vertically downward magnetic field is deflected 
toward the east. What is the sign of the charge on the particle? 
Q 2.  An electron experiences a magnetic force of magnitude 4.60 × 10
-15
 N, when moving at an angle 
of 60.0° with respect to a magnetic field of magnitude 3.50 × 10
-3
 T. Find the speed of the 
electron. 
Q 3.  A He
2+
 ion travels at right angles to a magnetic field of 0.80 T with a velocity of 10
5
 m/s. Find the 
magnitude of the magnetic force on the ion. 
Q 4.  An electron has velocity 
66
ˆˆ
v (2.0 10 m/s)i (3.0 10 m/s)j ? ? ? ?
?
.
 
Magnetic field present in the 
region is 
ˆˆ
B (0.030T)i (0.15T)j ??
?
. 
  (a) Find the force on electron.   
  (b) Repeat your calculation for a proton having the same velocity. 
Q 5.  An electron moves through a uniform magnetic field given by 
xx
ˆˆ
B B i (3B )j ??
?
. At a particular 
instant, the
 
electron has the velocity 
ˆˆ
v (2.0i 4.0j)m/s ??
?
and the magnetic force acting on it is 
19
ˆ
(6.4 10 N)k
?
? . Find B
x
.  
Q 6.  A charged particle carrying charge q = 1 ?C moves in uniform magnetic field with velocity v
1
 = 
10
6
 m/s at angle 45° with r-axis in the x-y plane and experiences a force 
1
F 5 2 mN ?
 
along the 
negative z-axis. When the same particle moves with velocity v
2
 = 10
6
 m/s along the z-axis it 
experiences a force F
2
 in y-direction. Find 
  (a) magnitude and direction of the magnetic field, (b) the magnitude of the force F
2
. 
Q 7.  A particle with charge 7.80 ?C is moving with velocity 
3
ˆ
v (3.80 10 m/s)j ? ? ?
?
.
 
The magnetic 
force on the particle is measured to be 
33
ˆˆ
F (7.60 10 N)i (5.20 10 N)k
??
? ? ? ? ?
?
. 
(a) Calculate the components of the magnetic field you can find from this information. 
(b) Are there components of the magnetic field that are not determined by the measurement of the 
force? Explain. 
(c) Calculate the scalar product B.F
??
. What is the angle between Band F
??
? 
Q 8.  Each of the lettered points at the comers of the cube in figure represents a positive charge q 
moving with a velocity of magnitude v in the direction indicated. The region in the figure is in a 
uniform magnetic field B
?
,
 
parallel to the x-axis and directed toward the right. Find the magnitude 
and direction of the force on each charge. 
Page 2


Exercises 
For JEE Main 
  Subjective Questions 
  Note You can take approximations in the answers. 
  Magnetic Force on a Charged Particle in Motion 
Q 1.  A particle initially moving towards south in a vertically downward magnetic field is deflected 
toward the east. What is the sign of the charge on the particle? 
Q 2.  An electron experiences a magnetic force of magnitude 4.60 × 10
-15
 N, when moving at an angle 
of 60.0° with respect to a magnetic field of magnitude 3.50 × 10
-3
 T. Find the speed of the 
electron. 
Q 3.  A He
2+
 ion travels at right angles to a magnetic field of 0.80 T with a velocity of 10
5
 m/s. Find the 
magnitude of the magnetic force on the ion. 
Q 4.  An electron has velocity 
66
ˆˆ
v (2.0 10 m/s)i (3.0 10 m/s)j ? ? ? ?
?
.
 
Magnetic field present in the 
region is 
ˆˆ
B (0.030T)i (0.15T)j ??
?
. 
  (a) Find the force on electron.   
  (b) Repeat your calculation for a proton having the same velocity. 
Q 5.  An electron moves through a uniform magnetic field given by 
xx
ˆˆ
B B i (3B )j ??
?
. At a particular 
instant, the
 
electron has the velocity 
ˆˆ
v (2.0i 4.0j)m/s ??
?
and the magnetic force acting on it is 
19
ˆ
(6.4 10 N)k
?
? . Find B
x
.  
Q 6.  A charged particle carrying charge q = 1 ?C moves in uniform magnetic field with velocity v
1
 = 
10
6
 m/s at angle 45° with r-axis in the x-y plane and experiences a force 
1
F 5 2 mN ?
 
along the 
negative z-axis. When the same particle moves with velocity v
2
 = 10
6
 m/s along the z-axis it 
experiences a force F
2
 in y-direction. Find 
  (a) magnitude and direction of the magnetic field, (b) the magnitude of the force F
2
. 
Q 7.  A particle with charge 7.80 ?C is moving with velocity 
3
ˆ
v (3.80 10 m/s)j ? ? ?
?
.
 
The magnetic 
force on the particle is measured to be 
33
ˆˆ
F (7.60 10 N)i (5.20 10 N)k
??
? ? ? ? ?
?
. 
(a) Calculate the components of the magnetic field you can find from this information. 
(b) Are there components of the magnetic field that are not determined by the measurement of the 
force? Explain. 
(c) Calculate the scalar product B.F
??
. What is the angle between Band F
??
? 
Q 8.  Each of the lettered points at the comers of the cube in figure represents a positive charge q 
moving with a velocity of magnitude v in the direction indicated. The region in the figure is in a 
uniform magnetic field B
?
,
 
parallel to the x-axis and directed toward the right. Find the magnitude 
and direction of the force on each charge. 
 
Motion of Charged Particle in Uniform Magnetic Field 
Q 9.  An electron in the beam of a TV picture tube is accelerated by a potential difference of 2.00 kV. 
Then, it passes through region of transverse magnetic field, where it moves in a circular arc with 
radius 0.180 m. What is the magnitude of the field? 
Q 10.  A deuteron (the nucleus of an isotope of hydrogen) has a mass of 3.34 × 10
-27
 kg and a charge of 
+e. The deuteron travels in a circular path with a radius of 6.96 mm in a magnetic field with 
magnitude 2.50 T. 
  (a) Find the speed of the deuteron. 
  (b) Find the time required for it to make half of a revolution. 
(c) Through what potential difference would the deuteron have to be accelerated to acquire this 
speed? 
Q 11.  A neutral particle is at rest in a uniform magnetic field B
?
. At time t = 0 it decays into two charged 
particles, each of mass m. 
(a) If the charge of one of the particles is +q, what is the charge of the other ? 
(b) The two particles move off in separate paths, both of them lie in the plane perpendicular to B
?
. 
At a later time the particles collide. Express the time from decay until collision in terms of m, B 
and q. 
Q 12.  An electron at point A in figure has a speed v
0
 = 1.41 × 10
6
 m/s. Find 
 
(a) the magnitude and direction of the magnetic field that will cause the electron to follow the 
semicircular path from A to B, 
  (b) the time required for the electron to move from A to B. 
Q 13.  A proton of charge e and mass m enters a uniform magnetic field 
ˆ
B Bi ?
?
with an initial velocity 
xy
ˆˆ
v v i v j ??
?
.
 
Find an expression in unit-vector notation for its velocity at time t. 
Q 14.  An electron gun G emits electrons of energy 2 keV travelling in the positive x-direction. The 
electrons are required to hit the spot of S where GS = 0.1 m, and the line GS makes an angle of 
60° with the x-axis as shown in figure. A uniform magnetic field B
?
 parallel to GS exists in the 
region outside the electron gun. Find the minimum value of B needed to make the electron hit S. 
Page 3


Exercises 
For JEE Main 
  Subjective Questions 
  Note You can take approximations in the answers. 
  Magnetic Force on a Charged Particle in Motion 
Q 1.  A particle initially moving towards south in a vertically downward magnetic field is deflected 
toward the east. What is the sign of the charge on the particle? 
Q 2.  An electron experiences a magnetic force of magnitude 4.60 × 10
-15
 N, when moving at an angle 
of 60.0° with respect to a magnetic field of magnitude 3.50 × 10
-3
 T. Find the speed of the 
electron. 
Q 3.  A He
2+
 ion travels at right angles to a magnetic field of 0.80 T with a velocity of 10
5
 m/s. Find the 
magnitude of the magnetic force on the ion. 
Q 4.  An electron has velocity 
66
ˆˆ
v (2.0 10 m/s)i (3.0 10 m/s)j ? ? ? ?
?
.
 
Magnetic field present in the 
region is 
ˆˆ
B (0.030T)i (0.15T)j ??
?
. 
  (a) Find the force on electron.   
  (b) Repeat your calculation for a proton having the same velocity. 
Q 5.  An electron moves through a uniform magnetic field given by 
xx
ˆˆ
B B i (3B )j ??
?
. At a particular 
instant, the
 
electron has the velocity 
ˆˆ
v (2.0i 4.0j)m/s ??
?
and the magnetic force acting on it is 
19
ˆ
(6.4 10 N)k
?
? . Find B
x
.  
Q 6.  A charged particle carrying charge q = 1 ?C moves in uniform magnetic field with velocity v
1
 = 
10
6
 m/s at angle 45° with r-axis in the x-y plane and experiences a force 
1
F 5 2 mN ?
 
along the 
negative z-axis. When the same particle moves with velocity v
2
 = 10
6
 m/s along the z-axis it 
experiences a force F
2
 in y-direction. Find 
  (a) magnitude and direction of the magnetic field, (b) the magnitude of the force F
2
. 
Q 7.  A particle with charge 7.80 ?C is moving with velocity 
3
ˆ
v (3.80 10 m/s)j ? ? ?
?
.
 
The magnetic 
force on the particle is measured to be 
33
ˆˆ
F (7.60 10 N)i (5.20 10 N)k
??
? ? ? ? ?
?
. 
(a) Calculate the components of the magnetic field you can find from this information. 
(b) Are there components of the magnetic field that are not determined by the measurement of the 
force? Explain. 
(c) Calculate the scalar product B.F
??
. What is the angle between Band F
??
? 
Q 8.  Each of the lettered points at the comers of the cube in figure represents a positive charge q 
moving with a velocity of magnitude v in the direction indicated. The region in the figure is in a 
uniform magnetic field B
?
,
 
parallel to the x-axis and directed toward the right. Find the magnitude 
and direction of the force on each charge. 
 
Motion of Charged Particle in Uniform Magnetic Field 
Q 9.  An electron in the beam of a TV picture tube is accelerated by a potential difference of 2.00 kV. 
Then, it passes through region of transverse magnetic field, where it moves in a circular arc with 
radius 0.180 m. What is the magnitude of the field? 
Q 10.  A deuteron (the nucleus of an isotope of hydrogen) has a mass of 3.34 × 10
-27
 kg and a charge of 
+e. The deuteron travels in a circular path with a radius of 6.96 mm in a magnetic field with 
magnitude 2.50 T. 
  (a) Find the speed of the deuteron. 
  (b) Find the time required for it to make half of a revolution. 
(c) Through what potential difference would the deuteron have to be accelerated to acquire this 
speed? 
Q 11.  A neutral particle is at rest in a uniform magnetic field B
?
. At time t = 0 it decays into two charged 
particles, each of mass m. 
(a) If the charge of one of the particles is +q, what is the charge of the other ? 
(b) The two particles move off in separate paths, both of them lie in the plane perpendicular to B
?
. 
At a later time the particles collide. Express the time from decay until collision in terms of m, B 
and q. 
Q 12.  An electron at point A in figure has a speed v
0
 = 1.41 × 10
6
 m/s. Find 
 
(a) the magnitude and direction of the magnetic field that will cause the electron to follow the 
semicircular path from A to B, 
  (b) the time required for the electron to move from A to B. 
Q 13.  A proton of charge e and mass m enters a uniform magnetic field 
ˆ
B Bi ?
?
with an initial velocity 
xy
ˆˆ
v v i v j ??
?
.
 
Find an expression in unit-vector notation for its velocity at time t. 
Q 14.  An electron gun G emits electrons of energy 2 keV travelling in the positive x-direction. The 
electrons are required to hit the spot of S where GS = 0.1 m, and the line GS makes an angle of 
60° with the x-axis as shown in figure. A uniform magnetic field B
?
 parallel to GS exists in the 
region outside the electron gun. Find the minimum value of B needed to make the electron hit S. 
 
Q 15.  The region between x - 0 and x = L is filled with uniform steady magnetic field 
0
ˆ
Bk .
 
A particle of 
mass m, positive charge q and velocity 
0
ˆ
vi
 
travels along x-axis and enters the region of the 
magnetic field. 
Neglect the gravity throughout the question. 
(a) Find the value of L if the particle emerges from the region of magnetic field with its final 
velocity at an angle 30° to its initial velocity. 
(b) Find the final velocity of the particle and the time spent by it in the magnetic field, if the 
magnetic field now extends up to 2.1 L. 
  Motion of Charged Particle in Electric and Magnetic Fields 
Q 16.  A proton moves at a constant velocity of 50 m/s along the x-axis, in uniform electric and magnetic 
fields. The magnetic field is 
ˆ
B (2.0mT)j ?
?
. What is the electric field? 
Q 17.  A particle having mass m and charge q is released from the origin in a region in which electric 
field and magnetic field are given by 
  
00
ˆˆ
B B j and E E k ? ? ?
??
 
Find the y- component of the velocity and the speed of the particle as a function of its z-
coordinate. 
Q 18.  Protons move rectilinearly in the region of space where there are uniform mutually perpendicular 
electric and magnetic fields E and B. The trajectory of protons lies in the plane xz as shown in the 
figure and forms an angle ?
 
with x-axis. Find the pitch of the helical trajectory along which the 
protons will move after the electric field is switched off. 
 
  Magnetic Force on Current Carrying Wire 
Q 19.  A horizontal rod 0.200 m long is mounted on a balance and carries a current. At the location of the 
rod a uniform horizontal magnetic field has magnitude 0.067 T and direction perpendicular to the 
rod. The magnetic force on the rod is measured by the balance and is found to be 0.13 N. What is 
the current? 
Q 20.  A wire of 62.0 cm length and 13.0 g mass is suspended by a pair of flexible leads in a uniform 
magnetic field of magnitude 0.440 T in figure. What are the magnitude and direction of the current 
required to remove the tension in the supporting leads? Take g = 10 m/s
2
. 
Page 4


Exercises 
For JEE Main 
  Subjective Questions 
  Note You can take approximations in the answers. 
  Magnetic Force on a Charged Particle in Motion 
Q 1.  A particle initially moving towards south in a vertically downward magnetic field is deflected 
toward the east. What is the sign of the charge on the particle? 
Q 2.  An electron experiences a magnetic force of magnitude 4.60 × 10
-15
 N, when moving at an angle 
of 60.0° with respect to a magnetic field of magnitude 3.50 × 10
-3
 T. Find the speed of the 
electron. 
Q 3.  A He
2+
 ion travels at right angles to a magnetic field of 0.80 T with a velocity of 10
5
 m/s. Find the 
magnitude of the magnetic force on the ion. 
Q 4.  An electron has velocity 
66
ˆˆ
v (2.0 10 m/s)i (3.0 10 m/s)j ? ? ? ?
?
.
 
Magnetic field present in the 
region is 
ˆˆ
B (0.030T)i (0.15T)j ??
?
. 
  (a) Find the force on electron.   
  (b) Repeat your calculation for a proton having the same velocity. 
Q 5.  An electron moves through a uniform magnetic field given by 
xx
ˆˆ
B B i (3B )j ??
?
. At a particular 
instant, the
 
electron has the velocity 
ˆˆ
v (2.0i 4.0j)m/s ??
?
and the magnetic force acting on it is 
19
ˆ
(6.4 10 N)k
?
? . Find B
x
.  
Q 6.  A charged particle carrying charge q = 1 ?C moves in uniform magnetic field with velocity v
1
 = 
10
6
 m/s at angle 45° with r-axis in the x-y plane and experiences a force 
1
F 5 2 mN ?
 
along the 
negative z-axis. When the same particle moves with velocity v
2
 = 10
6
 m/s along the z-axis it 
experiences a force F
2
 in y-direction. Find 
  (a) magnitude and direction of the magnetic field, (b) the magnitude of the force F
2
. 
Q 7.  A particle with charge 7.80 ?C is moving with velocity 
3
ˆ
v (3.80 10 m/s)j ? ? ?
?
.
 
The magnetic 
force on the particle is measured to be 
33
ˆˆ
F (7.60 10 N)i (5.20 10 N)k
??
? ? ? ? ?
?
. 
(a) Calculate the components of the magnetic field you can find from this information. 
(b) Are there components of the magnetic field that are not determined by the measurement of the 
force? Explain. 
(c) Calculate the scalar product B.F
??
. What is the angle between Band F
??
? 
Q 8.  Each of the lettered points at the comers of the cube in figure represents a positive charge q 
moving with a velocity of magnitude v in the direction indicated. The region in the figure is in a 
uniform magnetic field B
?
,
 
parallel to the x-axis and directed toward the right. Find the magnitude 
and direction of the force on each charge. 
 
Motion of Charged Particle in Uniform Magnetic Field 
Q 9.  An electron in the beam of a TV picture tube is accelerated by a potential difference of 2.00 kV. 
Then, it passes through region of transverse magnetic field, where it moves in a circular arc with 
radius 0.180 m. What is the magnitude of the field? 
Q 10.  A deuteron (the nucleus of an isotope of hydrogen) has a mass of 3.34 × 10
-27
 kg and a charge of 
+e. The deuteron travels in a circular path with a radius of 6.96 mm in a magnetic field with 
magnitude 2.50 T. 
  (a) Find the speed of the deuteron. 
  (b) Find the time required for it to make half of a revolution. 
(c) Through what potential difference would the deuteron have to be accelerated to acquire this 
speed? 
Q 11.  A neutral particle is at rest in a uniform magnetic field B
?
. At time t = 0 it decays into two charged 
particles, each of mass m. 
(a) If the charge of one of the particles is +q, what is the charge of the other ? 
(b) The two particles move off in separate paths, both of them lie in the plane perpendicular to B
?
. 
At a later time the particles collide. Express the time from decay until collision in terms of m, B 
and q. 
Q 12.  An electron at point A in figure has a speed v
0
 = 1.41 × 10
6
 m/s. Find 
 
(a) the magnitude and direction of the magnetic field that will cause the electron to follow the 
semicircular path from A to B, 
  (b) the time required for the electron to move from A to B. 
Q 13.  A proton of charge e and mass m enters a uniform magnetic field 
ˆ
B Bi ?
?
with an initial velocity 
xy
ˆˆ
v v i v j ??
?
.
 
Find an expression in unit-vector notation for its velocity at time t. 
Q 14.  An electron gun G emits electrons of energy 2 keV travelling in the positive x-direction. The 
electrons are required to hit the spot of S where GS = 0.1 m, and the line GS makes an angle of 
60° with the x-axis as shown in figure. A uniform magnetic field B
?
 parallel to GS exists in the 
region outside the electron gun. Find the minimum value of B needed to make the electron hit S. 
 
Q 15.  The region between x - 0 and x = L is filled with uniform steady magnetic field 
0
ˆ
Bk .
 
A particle of 
mass m, positive charge q and velocity 
0
ˆ
vi
 
travels along x-axis and enters the region of the 
magnetic field. 
Neglect the gravity throughout the question. 
(a) Find the value of L if the particle emerges from the region of magnetic field with its final 
velocity at an angle 30° to its initial velocity. 
(b) Find the final velocity of the particle and the time spent by it in the magnetic field, if the 
magnetic field now extends up to 2.1 L. 
  Motion of Charged Particle in Electric and Magnetic Fields 
Q 16.  A proton moves at a constant velocity of 50 m/s along the x-axis, in uniform electric and magnetic 
fields. The magnetic field is 
ˆ
B (2.0mT)j ?
?
. What is the electric field? 
Q 17.  A particle having mass m and charge q is released from the origin in a region in which electric 
field and magnetic field are given by 
  
00
ˆˆ
B B j and E E k ? ? ?
??
 
Find the y- component of the velocity and the speed of the particle as a function of its z-
coordinate. 
Q 18.  Protons move rectilinearly in the region of space where there are uniform mutually perpendicular 
electric and magnetic fields E and B. The trajectory of protons lies in the plane xz as shown in the 
figure and forms an angle ?
 
with x-axis. Find the pitch of the helical trajectory along which the 
protons will move after the electric field is switched off. 
 
  Magnetic Force on Current Carrying Wire 
Q 19.  A horizontal rod 0.200 m long is mounted on a balance and carries a current. At the location of the 
rod a uniform horizontal magnetic field has magnitude 0.067 T and direction perpendicular to the 
rod. The magnetic force on the rod is measured by the balance and is found to be 0.13 N. What is 
the current? 
Q 20.  A wire of 62.0 cm length and 13.0 g mass is suspended by a pair of flexible leads in a uniform 
magnetic field of magnitude 0.440 T in figure. What are the magnitude and direction of the current 
required to remove the tension in the supporting leads? Take g = 10 m/s
2
. 
 
Q 21.  A thin, 50.0 cm long metal bar with mass 750 g rests on, but is not attached to, two metallic 
supports in a 0.450 T magnetic field, as shown in figure. A battery and a resistance R = 25.0 ? in 
series are connected to the supports. 
 
(a) What is the largest voltage the battery can have without breaking the circuit at the supports? 
(b) The battery voltage has this maximum value calculated. Decreasing the resistance to 2.0 ?, 
find the initial acceleration of the bar. 
Q 22.  A wire along the x-axis carries a current of 3.50 A in the negative direction. Calculate the force 
(expressed in terms of unit vectors) on a 1.00 cm section of the wire exerted by these magnetic 
fields 
 (a) 
ˆ
B (0.65T)j ??
?
   (b) 
ˆ
B (0.56T)k ??
?
 
 (c) 
ˆ
B (0.31T)i ??
?
  (d) 
ˆˆ
B (0.33T)i (0.28T)k ? ? ?
?
 
  (e) 
ˆˆ
B (0.74T)j (0.36T)k ? ? ?
?
 
Q 23.  In figure, the cube is 40.0 cm on each edge. Four straight segments of wire ab, bc, cd and da form 
a closed loop that carries a current I = 5.00 A, in the direction shown. A uniform magnetic field of 
magnitude B = 0.020 T is in the positive y-direction. Determine the magnitude and direction of the 
magnetic force on each segment. 
*  
Magnetic Dipole 
Q 24.  A circular loop of wire having a radius of 8.0 cm carries a current of 0.20 A. A vector of unit 
length and parallel to the dipole moment M
?
of the loop is given by 
ˆˆ
0.60i 0.80j ? . If the loop is 
located in uniform magnetic field given by
ˆˆ
B (0.25T)i 0.30T)k ??
?
 
find, 
(a) the torque on the loop and  (b) the magnetic potential energy of the loop. 
Page 5


Exercises 
For JEE Main 
  Subjective Questions 
  Note You can take approximations in the answers. 
  Magnetic Force on a Charged Particle in Motion 
Q 1.  A particle initially moving towards south in a vertically downward magnetic field is deflected 
toward the east. What is the sign of the charge on the particle? 
Q 2.  An electron experiences a magnetic force of magnitude 4.60 × 10
-15
 N, when moving at an angle 
of 60.0° with respect to a magnetic field of magnitude 3.50 × 10
-3
 T. Find the speed of the 
electron. 
Q 3.  A He
2+
 ion travels at right angles to a magnetic field of 0.80 T with a velocity of 10
5
 m/s. Find the 
magnitude of the magnetic force on the ion. 
Q 4.  An electron has velocity 
66
ˆˆ
v (2.0 10 m/s)i (3.0 10 m/s)j ? ? ? ?
?
.
 
Magnetic field present in the 
region is 
ˆˆ
B (0.030T)i (0.15T)j ??
?
. 
  (a) Find the force on electron.   
  (b) Repeat your calculation for a proton having the same velocity. 
Q 5.  An electron moves through a uniform magnetic field given by 
xx
ˆˆ
B B i (3B )j ??
?
. At a particular 
instant, the
 
electron has the velocity 
ˆˆ
v (2.0i 4.0j)m/s ??
?
and the magnetic force acting on it is 
19
ˆ
(6.4 10 N)k
?
? . Find B
x
.  
Q 6.  A charged particle carrying charge q = 1 ?C moves in uniform magnetic field with velocity v
1
 = 
10
6
 m/s at angle 45° with r-axis in the x-y plane and experiences a force 
1
F 5 2 mN ?
 
along the 
negative z-axis. When the same particle moves with velocity v
2
 = 10
6
 m/s along the z-axis it 
experiences a force F
2
 in y-direction. Find 
  (a) magnitude and direction of the magnetic field, (b) the magnitude of the force F
2
. 
Q 7.  A particle with charge 7.80 ?C is moving with velocity 
3
ˆ
v (3.80 10 m/s)j ? ? ?
?
.
 
The magnetic 
force on the particle is measured to be 
33
ˆˆ
F (7.60 10 N)i (5.20 10 N)k
??
? ? ? ? ?
?
. 
(a) Calculate the components of the magnetic field you can find from this information. 
(b) Are there components of the magnetic field that are not determined by the measurement of the 
force? Explain. 
(c) Calculate the scalar product B.F
??
. What is the angle between Band F
??
? 
Q 8.  Each of the lettered points at the comers of the cube in figure represents a positive charge q 
moving with a velocity of magnitude v in the direction indicated. The region in the figure is in a 
uniform magnetic field B
?
,
 
parallel to the x-axis and directed toward the right. Find the magnitude 
and direction of the force on each charge. 
 
Motion of Charged Particle in Uniform Magnetic Field 
Q 9.  An electron in the beam of a TV picture tube is accelerated by a potential difference of 2.00 kV. 
Then, it passes through region of transverse magnetic field, where it moves in a circular arc with 
radius 0.180 m. What is the magnitude of the field? 
Q 10.  A deuteron (the nucleus of an isotope of hydrogen) has a mass of 3.34 × 10
-27
 kg and a charge of 
+e. The deuteron travels in a circular path with a radius of 6.96 mm in a magnetic field with 
magnitude 2.50 T. 
  (a) Find the speed of the deuteron. 
  (b) Find the time required for it to make half of a revolution. 
(c) Through what potential difference would the deuteron have to be accelerated to acquire this 
speed? 
Q 11.  A neutral particle is at rest in a uniform magnetic field B
?
. At time t = 0 it decays into two charged 
particles, each of mass m. 
(a) If the charge of one of the particles is +q, what is the charge of the other ? 
(b) The two particles move off in separate paths, both of them lie in the plane perpendicular to B
?
. 
At a later time the particles collide. Express the time from decay until collision in terms of m, B 
and q. 
Q 12.  An electron at point A in figure has a speed v
0
 = 1.41 × 10
6
 m/s. Find 
 
(a) the magnitude and direction of the magnetic field that will cause the electron to follow the 
semicircular path from A to B, 
  (b) the time required for the electron to move from A to B. 
Q 13.  A proton of charge e and mass m enters a uniform magnetic field 
ˆ
B Bi ?
?
with an initial velocity 
xy
ˆˆ
v v i v j ??
?
.
 
Find an expression in unit-vector notation for its velocity at time t. 
Q 14.  An electron gun G emits electrons of energy 2 keV travelling in the positive x-direction. The 
electrons are required to hit the spot of S where GS = 0.1 m, and the line GS makes an angle of 
60° with the x-axis as shown in figure. A uniform magnetic field B
?
 parallel to GS exists in the 
region outside the electron gun. Find the minimum value of B needed to make the electron hit S. 
 
Q 15.  The region between x - 0 and x = L is filled with uniform steady magnetic field 
0
ˆ
Bk .
 
A particle of 
mass m, positive charge q and velocity 
0
ˆ
vi
 
travels along x-axis and enters the region of the 
magnetic field. 
Neglect the gravity throughout the question. 
(a) Find the value of L if the particle emerges from the region of magnetic field with its final 
velocity at an angle 30° to its initial velocity. 
(b) Find the final velocity of the particle and the time spent by it in the magnetic field, if the 
magnetic field now extends up to 2.1 L. 
  Motion of Charged Particle in Electric and Magnetic Fields 
Q 16.  A proton moves at a constant velocity of 50 m/s along the x-axis, in uniform electric and magnetic 
fields. The magnetic field is 
ˆ
B (2.0mT)j ?
?
. What is the electric field? 
Q 17.  A particle having mass m and charge q is released from the origin in a region in which electric 
field and magnetic field are given by 
  
00
ˆˆ
B B j and E E k ? ? ?
??
 
Find the y- component of the velocity and the speed of the particle as a function of its z-
coordinate. 
Q 18.  Protons move rectilinearly in the region of space where there are uniform mutually perpendicular 
electric and magnetic fields E and B. The trajectory of protons lies in the plane xz as shown in the 
figure and forms an angle ?
 
with x-axis. Find the pitch of the helical trajectory along which the 
protons will move after the electric field is switched off. 
 
  Magnetic Force on Current Carrying Wire 
Q 19.  A horizontal rod 0.200 m long is mounted on a balance and carries a current. At the location of the 
rod a uniform horizontal magnetic field has magnitude 0.067 T and direction perpendicular to the 
rod. The magnetic force on the rod is measured by the balance and is found to be 0.13 N. What is 
the current? 
Q 20.  A wire of 62.0 cm length and 13.0 g mass is suspended by a pair of flexible leads in a uniform 
magnetic field of magnitude 0.440 T in figure. What are the magnitude and direction of the current 
required to remove the tension in the supporting leads? Take g = 10 m/s
2
. 
 
Q 21.  A thin, 50.0 cm long metal bar with mass 750 g rests on, but is not attached to, two metallic 
supports in a 0.450 T magnetic field, as shown in figure. A battery and a resistance R = 25.0 ? in 
series are connected to the supports. 
 
(a) What is the largest voltage the battery can have without breaking the circuit at the supports? 
(b) The battery voltage has this maximum value calculated. Decreasing the resistance to 2.0 ?, 
find the initial acceleration of the bar. 
Q 22.  A wire along the x-axis carries a current of 3.50 A in the negative direction. Calculate the force 
(expressed in terms of unit vectors) on a 1.00 cm section of the wire exerted by these magnetic 
fields 
 (a) 
ˆ
B (0.65T)j ??
?
   (b) 
ˆ
B (0.56T)k ??
?
 
 (c) 
ˆ
B (0.31T)i ??
?
  (d) 
ˆˆ
B (0.33T)i (0.28T)k ? ? ?
?
 
  (e) 
ˆˆ
B (0.74T)j (0.36T)k ? ? ?
?
 
Q 23.  In figure, the cube is 40.0 cm on each edge. Four straight segments of wire ab, bc, cd and da form 
a closed loop that carries a current I = 5.00 A, in the direction shown. A uniform magnetic field of 
magnitude B = 0.020 T is in the positive y-direction. Determine the magnitude and direction of the 
magnetic force on each segment. 
*  
Magnetic Dipole 
Q 24.  A circular loop of wire having a radius of 8.0 cm carries a current of 0.20 A. A vector of unit 
length and parallel to the dipole moment M
?
of the loop is given by 
ˆˆ
0.60i 0.80j ? . If the loop is 
located in uniform magnetic field given by
ˆˆ
B (0.25T)i 0.30T)k ??
?
 
find, 
(a) the torque on the loop and  (b) the magnetic potential energy of the loop. 
Q 25.  A length L of wire carries a current i. Show that if the wire is formed into a circular coil, then the 
maximum torque in a given magnetic field is developed when the coil has one turn only, and that 
maximum torque has the magnitude ? = L
2
 iB/4 ?. 
Q 26.  Find the ratio of magnetic dipole moment and magnetic field at the centre of a disc. Radius of disc 
is R and it is rotating at constant angular speed ? about its axis. The disc is insulating and 
uniformly charged. 
Q 27.  A magnetic dipole with a dipole moment of magnitude 0.020 J/T is released from rest in a uniform 
magnetic field of magnitude 52 mT. The rotation of the dipole due to the magnetic force on it is 
unimpeded. When the dipole rotates through the orientations where its dipole moment is aligned 
with the magnetic field, its kinetic energy is 0.80 mJ. 
(a) What is the initial angle between the dipole moment and the magnetic field? 
(b) What is the angle when the dipole is next (momentarily) at rest? 
Q 28.  A coil with magnetic moment 1.45 A-m
2
 is oriented initially with its magnetic moment antiparallel 
to a uniform 0.835 T magnetic field. What is the change in potential energy of the coil when it is 
rotated 180° so that its magnetic moment is parallel to the field? 
Q 29.  In the Bohr model of the hydrogen atom, in the lowest energy state the electron revolves round the 
proton at a speed of 2.2 × 10
6
 m/s in a circular orbit of radius 5.3 × 10
-11
 m. 
(a) What is the orbital period of the electron? 
(b) If the orbiting electron is considered to be a current loop, what is the current I ? 
(c) What is the magnetic moment of the atom due to the motion of the electron? 
Q 30.  A conductor carries a constant current I along the closed path abcdefgha involving 8 of the 12 
edges each of length l. Find the magnetic dipole moment of the closed path. 
 
Q 31.  Given figure shows a coil bent with all edges of length 1 m and carrying a current of 1 A. There 
exists in space a uniform magnetic field of 2 T in positive y-direction. Find the torque on the loop. 
 
  Applications of Biot Savart's Law 
Q 32.  A very long wire carrying a current I = 5.0 A is bent at right angles. Find the magnetic induction at 
a point lying on a perpendicular normal to the plane of the wire drawn through the point of 
bending, at a distance l = 35 cm from it.