DC Pandey Solutions (JEE Advance): Electromagnetic Induction- 2 | DC Pandey Solutions for JEE Physics PDF Download

 Page 1


For JEE Advanced 
  More than One Correct Options 
 
Q 1.  The loop shown moves with a velocity v in a uniform magnetic field of magnitude B, directed into 
the paper. The potential difference between points P and Q is e. Then 
 
  (a) 
1
e BLv
2
?
      
(b) e = BLv 
  (c) P is positive with respect to Q  (d) Q is positive with respect to P 
Q 2.  In infinitely long wire is placed near a square loop as shown in figure. Choose the correct options. 
 
  (a) The mutual inductance between the two is 
0
a
ln(2)
2
?
?
 
  (b) The mutual inductance between the two is 
2
0
a
ln(2)
2
?
?
 
(c) If a constant current is passed in the straight wire in upward direction and loop is brought close 
to the wire then induced current in the loop is clockwise 
  (d) In the above condition, induced current in the loop is anticlockwise 
Q 3.  Choose the correct options 
  (a) SI unit of magnetic flux is henry-ampere  
  (b) SI unit of coefficient of self-inductance is J/A 
  (c) SI unit of coefficient of self inductance is 
volt second
ampere
?
 
  (d) SI unit of magnetic induction is weber 
Q 4.  In the circuit shown in figure, circuit is closed at time t — 0. At time t = In (2) second 
 
  (a) rate of energy supplied by the battery is 16 J/s  
  (b) rate of heat dissipated across resistance is 8 J/s 
  (c) rate of heat dissipated across resistance is 16 J/s 
  (d)V
a 
- V
b
=4V  
Page 2


For JEE Advanced 
  More than One Correct Options 
 
Q 1.  The loop shown moves with a velocity v in a uniform magnetic field of magnitude B, directed into 
the paper. The potential difference between points P and Q is e. Then 
 
  (a) 
1
e BLv
2
?
      
(b) e = BLv 
  (c) P is positive with respect to Q  (d) Q is positive with respect to P 
Q 2.  In infinitely long wire is placed near a square loop as shown in figure. Choose the correct options. 
 
  (a) The mutual inductance between the two is 
0
a
ln(2)
2
?
?
 
  (b) The mutual inductance between the two is 
2
0
a
ln(2)
2
?
?
 
(c) If a constant current is passed in the straight wire in upward direction and loop is brought close 
to the wire then induced current in the loop is clockwise 
  (d) In the above condition, induced current in the loop is anticlockwise 
Q 3.  Choose the correct options 
  (a) SI unit of magnetic flux is henry-ampere  
  (b) SI unit of coefficient of self-inductance is J/A 
  (c) SI unit of coefficient of self inductance is 
volt second
ampere
?
 
  (d) SI unit of magnetic induction is weber 
Q 4.  In the circuit shown in figure, circuit is closed at time t — 0. At time t = In (2) second 
 
  (a) rate of energy supplied by the battery is 16 J/s  
  (b) rate of heat dissipated across resistance is 8 J/s 
  (c) rate of heat dissipated across resistance is 16 J/s 
  (d)V
a 
- V
b
=4V  
Q 5.  Two circular coils are placed adjacent to each other. Their planes are parallel and currents through 
them i
1
 and i
2
 are in same directions. Choose the correct options 
 
  (a) When A is brought near B, current i
2
 will decrease 
  (b) In the above process, current i
2
 will increase 
  (c) When current i
1
 is increased, current i
2
 will decrease   
  (d) In the above process, current i
2
 will increase 
Q 6.  A coil of area 2m
2
 and resistance 4 ?
 
is placed perpendicular to a uniform magnetic field of 4 T. 
The loop is rotated by 90° in 0.1 second. Choose the correct options. 
  (a) Average induced emf in the coil is 8 V 
  (b) Average induced current in the circuit is 20 A  
(c) 2 C charge will flow in the coil in above period   
(d) Heat produced in the coil in the above period can't be determined from the given data 
Q 7.  In L-C oscillations 
  (a) time period of oscillations is 
2
LC
?
  (b) maximum current in circuit is 
0
q
LC
 
  (c) maximum rate of change of current in circuit is 
0
q
LC
 
(d) maximum potential difference across the inductor is 
0
q
2C
.  
Here: q
0
 is maximum charge on capacitor. 
Q 8.  Magnetic field in a cylindrical region of radius R in inward direction is as shown in figure 
 
  (a) an electron will experience no force kept at (2R, 0,0) if magnetic field increases with time 
(b) in the above situation, electron will experience the force in negative y-axis 
(c) If a proton is kept at 
R
0, ,0
2
??
??
??
and magnetic field is decreasing, then it will experience the 
force in positive x-direction 
  (d) if a proton is kept at (-R, 0,0) and magnetic field is increasing, then it will experience force in 
 negative y-axis 
Q 9.  In the figure shown, q is in coulomb and t in second. At time t = 1 s 
 
  (a) V
a
 - V
b
 = 4V  (b) V
b 
- V
c 
= 1V  (c) V
c 
- V
d 
= 16V  (d) V
a 
- V
d 
= 20 V 
Page 3


For JEE Advanced 
  More than One Correct Options 
 
Q 1.  The loop shown moves with a velocity v in a uniform magnetic field of magnitude B, directed into 
the paper. The potential difference between points P and Q is e. Then 
 
  (a) 
1
e BLv
2
?
      
(b) e = BLv 
  (c) P is positive with respect to Q  (d) Q is positive with respect to P 
Q 2.  In infinitely long wire is placed near a square loop as shown in figure. Choose the correct options. 
 
  (a) The mutual inductance between the two is 
0
a
ln(2)
2
?
?
 
  (b) The mutual inductance between the two is 
2
0
a
ln(2)
2
?
?
 
(c) If a constant current is passed in the straight wire in upward direction and loop is brought close 
to the wire then induced current in the loop is clockwise 
  (d) In the above condition, induced current in the loop is anticlockwise 
Q 3.  Choose the correct options 
  (a) SI unit of magnetic flux is henry-ampere  
  (b) SI unit of coefficient of self-inductance is J/A 
  (c) SI unit of coefficient of self inductance is 
volt second
ampere
?
 
  (d) SI unit of magnetic induction is weber 
Q 4.  In the circuit shown in figure, circuit is closed at time t — 0. At time t = In (2) second 
 
  (a) rate of energy supplied by the battery is 16 J/s  
  (b) rate of heat dissipated across resistance is 8 J/s 
  (c) rate of heat dissipated across resistance is 16 J/s 
  (d)V
a 
- V
b
=4V  
Q 5.  Two circular coils are placed adjacent to each other. Their planes are parallel and currents through 
them i
1
 and i
2
 are in same directions. Choose the correct options 
 
  (a) When A is brought near B, current i
2
 will decrease 
  (b) In the above process, current i
2
 will increase 
  (c) When current i
1
 is increased, current i
2
 will decrease   
  (d) In the above process, current i
2
 will increase 
Q 6.  A coil of area 2m
2
 and resistance 4 ?
 
is placed perpendicular to a uniform magnetic field of 4 T. 
The loop is rotated by 90° in 0.1 second. Choose the correct options. 
  (a) Average induced emf in the coil is 8 V 
  (b) Average induced current in the circuit is 20 A  
(c) 2 C charge will flow in the coil in above period   
(d) Heat produced in the coil in the above period can't be determined from the given data 
Q 7.  In L-C oscillations 
  (a) time period of oscillations is 
2
LC
?
  (b) maximum current in circuit is 
0
q
LC
 
  (c) maximum rate of change of current in circuit is 
0
q
LC
 
(d) maximum potential difference across the inductor is 
0
q
2C
.  
Here: q
0
 is maximum charge on capacitor. 
Q 8.  Magnetic field in a cylindrical region of radius R in inward direction is as shown in figure 
 
  (a) an electron will experience no force kept at (2R, 0,0) if magnetic field increases with time 
(b) in the above situation, electron will experience the force in negative y-axis 
(c) If a proton is kept at 
R
0, ,0
2
??
??
??
and magnetic field is decreasing, then it will experience the 
force in positive x-direction 
  (d) if a proton is kept at (-R, 0,0) and magnetic field is increasing, then it will experience force in 
 negative y-axis 
Q 9.  In the figure shown, q is in coulomb and t in second. At time t = 1 s 
 
  (a) V
a
 - V
b
 = 4V  (b) V
b 
- V
c 
= 1V  (c) V
c 
- V
d 
= 16V  (d) V
a 
- V
d 
= 20 V 
Q 10.  An equilateral triangular conducting frame is rotated with angular velocity ? in uniform magnetic 
field B as shown. Side of triangle is l. Choose the correct options. 
 
  (a) V
a 
- V
c 
= 0   (b) V
a 
- V
c 
= 
2
Bl
2
?
 
(c) V
a 
- V
b 
= 
2
Bl
2
?
  (d) V
c 
- V
b
 =-
2
Bl
2
?
 
Answers 
  1. (a,c) 2. (a,c) 3. (a,c) 4. (a,b,d) 5. (a,c) 6. (b,c,d) 7. (b,c) 8. (b,c,d) 9. (a,b,c) 10. (a,c) 
Solutions 
1.  e = Bvl  
   where
y
 
  For polarity of this motional emf we can use right hand rule. 
2. (a) 
    
  (c) 
Wire produces magnetic field over the loop. If the loop is brought closer to the wire magnetic 
field passing through the loop increases. Hence induced current produces  magnetic field so, 
induced current is clockwise. 
3. 
 
(a) 
   
  So, SI unit of flux is Henry-ampere.  
  (b) 
  Hence, SI unit of L is 
4.  
Page 4


For JEE Advanced 
  More than One Correct Options 
 
Q 1.  The loop shown moves with a velocity v in a uniform magnetic field of magnitude B, directed into 
the paper. The potential difference between points P and Q is e. Then 
 
  (a) 
1
e BLv
2
?
      
(b) e = BLv 
  (c) P is positive with respect to Q  (d) Q is positive with respect to P 
Q 2.  In infinitely long wire is placed near a square loop as shown in figure. Choose the correct options. 
 
  (a) The mutual inductance between the two is 
0
a
ln(2)
2
?
?
 
  (b) The mutual inductance between the two is 
2
0
a
ln(2)
2
?
?
 
(c) If a constant current is passed in the straight wire in upward direction and loop is brought close 
to the wire then induced current in the loop is clockwise 
  (d) In the above condition, induced current in the loop is anticlockwise 
Q 3.  Choose the correct options 
  (a) SI unit of magnetic flux is henry-ampere  
  (b) SI unit of coefficient of self-inductance is J/A 
  (c) SI unit of coefficient of self inductance is 
volt second
ampere
?
 
  (d) SI unit of magnetic induction is weber 
Q 4.  In the circuit shown in figure, circuit is closed at time t — 0. At time t = In (2) second 
 
  (a) rate of energy supplied by the battery is 16 J/s  
  (b) rate of heat dissipated across resistance is 8 J/s 
  (c) rate of heat dissipated across resistance is 16 J/s 
  (d)V
a 
- V
b
=4V  
Q 5.  Two circular coils are placed adjacent to each other. Their planes are parallel and currents through 
them i
1
 and i
2
 are in same directions. Choose the correct options 
 
  (a) When A is brought near B, current i
2
 will decrease 
  (b) In the above process, current i
2
 will increase 
  (c) When current i
1
 is increased, current i
2
 will decrease   
  (d) In the above process, current i
2
 will increase 
Q 6.  A coil of area 2m
2
 and resistance 4 ?
 
is placed perpendicular to a uniform magnetic field of 4 T. 
The loop is rotated by 90° in 0.1 second. Choose the correct options. 
  (a) Average induced emf in the coil is 8 V 
  (b) Average induced current in the circuit is 20 A  
(c) 2 C charge will flow in the coil in above period   
(d) Heat produced in the coil in the above period can't be determined from the given data 
Q 7.  In L-C oscillations 
  (a) time period of oscillations is 
2
LC
?
  (b) maximum current in circuit is 
0
q
LC
 
  (c) maximum rate of change of current in circuit is 
0
q
LC
 
(d) maximum potential difference across the inductor is 
0
q
2C
.  
Here: q
0
 is maximum charge on capacitor. 
Q 8.  Magnetic field in a cylindrical region of radius R in inward direction is as shown in figure 
 
  (a) an electron will experience no force kept at (2R, 0,0) if magnetic field increases with time 
(b) in the above situation, electron will experience the force in negative y-axis 
(c) If a proton is kept at 
R
0, ,0
2
??
??
??
and magnetic field is decreasing, then it will experience the 
force in positive x-direction 
  (d) if a proton is kept at (-R, 0,0) and magnetic field is increasing, then it will experience force in 
 negative y-axis 
Q 9.  In the figure shown, q is in coulomb and t in second. At time t = 1 s 
 
  (a) V
a
 - V
b
 = 4V  (b) V
b 
- V
c 
= 1V  (c) V
c 
- V
d 
= 16V  (d) V
a 
- V
d 
= 20 V 
Q 10.  An equilateral triangular conducting frame is rotated with angular velocity ? in uniform magnetic 
field B as shown. Side of triangle is l. Choose the correct options. 
 
  (a) V
a 
- V
c 
= 0   (b) V
a 
- V
c 
= 
2
Bl
2
?
 
(c) V
a 
- V
b 
= 
2
Bl
2
?
  (d) V
c 
- V
b
 =-
2
Bl
2
?
 
Answers 
  1. (a,c) 2. (a,c) 3. (a,c) 4. (a,b,d) 5. (a,c) 6. (b,c,d) 7. (b,c) 8. (b,c,d) 9. (a,b,c) 10. (a,c) 
Solutions 
1.  e = Bvl  
   where
y
 
  For polarity of this motional emf we can use right hand rule. 
2. (a) 
    
  (c) 
Wire produces magnetic field over the loop. If the loop is brought closer to the wire magnetic 
field passing through the loop increases. Hence induced current produces  magnetic field so, 
induced current is clockwise. 
3. 
 
(a) 
   
  So, SI unit of flux is Henry-ampere.  
  (b) 
  Hence, SI unit of L is 
4.  
    
  Hence the given time is half life time. 
   
Rate of energy supplied by battery  
  = Ei = 8 × 2 = 16 J/s  
  P
R 
= i
2
R = (2)
2
(2) = 8J/s  
  V
a 
- V
b 
= E - iR = 8 – 2 × 2 = 4V 
5.  According to Lenz's law, induced effects always oppose the change i
1
 and i
2
 both are in same 
direction.  
Hence magnetic lines from B due to both currents are from right to left. By bringing A closer to B 
or increasing i
1
 right to left magnetic field from B will increase. So i
2
 should decrease. 
6.  ?
i
 = BS cos 0° = (4) (2) = 8 Wb  
  ?
f
 = BS cos 90° = 0 
   ? ?
 
= 8Wb 
    
This current is not constant. So, we cannot find the heat generated unless current function with 
time is not known. 
7.  
   
8.  If magnetic field increase than induced electric lines are anti-clockwise. If  magnetic field 
decreases, then induced electric lines are clockwise (both inside and outside the cylindrical 
region). 
On positive charge, force is in the direction of E
?
. On negative charge, force is in the opposite 
direction of E
?
.  
9.  q = 2t
2
 
    
  At t = 1s, q = 2C, i = 4A 
   
  V
c 
- V
d
 = iR = 4 × 4 = l6V  
  V
a
 - V
d
 is summation of above three i.e., 21 V. 
Page 5


For JEE Advanced 
  More than One Correct Options 
 
Q 1.  The loop shown moves with a velocity v in a uniform magnetic field of magnitude B, directed into 
the paper. The potential difference between points P and Q is e. Then 
 
  (a) 
1
e BLv
2
?
      
(b) e = BLv 
  (c) P is positive with respect to Q  (d) Q is positive with respect to P 
Q 2.  In infinitely long wire is placed near a square loop as shown in figure. Choose the correct options. 
 
  (a) The mutual inductance between the two is 
0
a
ln(2)
2
?
?
 
  (b) The mutual inductance between the two is 
2
0
a
ln(2)
2
?
?
 
(c) If a constant current is passed in the straight wire in upward direction and loop is brought close 
to the wire then induced current in the loop is clockwise 
  (d) In the above condition, induced current in the loop is anticlockwise 
Q 3.  Choose the correct options 
  (a) SI unit of magnetic flux is henry-ampere  
  (b) SI unit of coefficient of self-inductance is J/A 
  (c) SI unit of coefficient of self inductance is 
volt second
ampere
?
 
  (d) SI unit of magnetic induction is weber 
Q 4.  In the circuit shown in figure, circuit is closed at time t — 0. At time t = In (2) second 
 
  (a) rate of energy supplied by the battery is 16 J/s  
  (b) rate of heat dissipated across resistance is 8 J/s 
  (c) rate of heat dissipated across resistance is 16 J/s 
  (d)V
a 
- V
b
=4V  
Q 5.  Two circular coils are placed adjacent to each other. Their planes are parallel and currents through 
them i
1
 and i
2
 are in same directions. Choose the correct options 
 
  (a) When A is brought near B, current i
2
 will decrease 
  (b) In the above process, current i
2
 will increase 
  (c) When current i
1
 is increased, current i
2
 will decrease   
  (d) In the above process, current i
2
 will increase 
Q 6.  A coil of area 2m
2
 and resistance 4 ?
 
is placed perpendicular to a uniform magnetic field of 4 T. 
The loop is rotated by 90° in 0.1 second. Choose the correct options. 
  (a) Average induced emf in the coil is 8 V 
  (b) Average induced current in the circuit is 20 A  
(c) 2 C charge will flow in the coil in above period   
(d) Heat produced in the coil in the above period can't be determined from the given data 
Q 7.  In L-C oscillations 
  (a) time period of oscillations is 
2
LC
?
  (b) maximum current in circuit is 
0
q
LC
 
  (c) maximum rate of change of current in circuit is 
0
q
LC
 
(d) maximum potential difference across the inductor is 
0
q
2C
.  
Here: q
0
 is maximum charge on capacitor. 
Q 8.  Magnetic field in a cylindrical region of radius R in inward direction is as shown in figure 
 
  (a) an electron will experience no force kept at (2R, 0,0) if magnetic field increases with time 
(b) in the above situation, electron will experience the force in negative y-axis 
(c) If a proton is kept at 
R
0, ,0
2
??
??
??
and magnetic field is decreasing, then it will experience the 
force in positive x-direction 
  (d) if a proton is kept at (-R, 0,0) and magnetic field is increasing, then it will experience force in 
 negative y-axis 
Q 9.  In the figure shown, q is in coulomb and t in second. At time t = 1 s 
 
  (a) V
a
 - V
b
 = 4V  (b) V
b 
- V
c 
= 1V  (c) V
c 
- V
d 
= 16V  (d) V
a 
- V
d 
= 20 V 
Q 10.  An equilateral triangular conducting frame is rotated with angular velocity ? in uniform magnetic 
field B as shown. Side of triangle is l. Choose the correct options. 
 
  (a) V
a 
- V
c 
= 0   (b) V
a 
- V
c 
= 
2
Bl
2
?
 
(c) V
a 
- V
b 
= 
2
Bl
2
?
  (d) V
c 
- V
b
 =-
2
Bl
2
?
 
Answers 
  1. (a,c) 2. (a,c) 3. (a,c) 4. (a,b,d) 5. (a,c) 6. (b,c,d) 7. (b,c) 8. (b,c,d) 9. (a,b,c) 10. (a,c) 
Solutions 
1.  e = Bvl  
   where
y
 
  For polarity of this motional emf we can use right hand rule. 
2. (a) 
    
  (c) 
Wire produces magnetic field over the loop. If the loop is brought closer to the wire magnetic 
field passing through the loop increases. Hence induced current produces  magnetic field so, 
induced current is clockwise. 
3. 
 
(a) 
   
  So, SI unit of flux is Henry-ampere.  
  (b) 
  Hence, SI unit of L is 
4.  
    
  Hence the given time is half life time. 
   
Rate of energy supplied by battery  
  = Ei = 8 × 2 = 16 J/s  
  P
R 
= i
2
R = (2)
2
(2) = 8J/s  
  V
a 
- V
b 
= E - iR = 8 – 2 × 2 = 4V 
5.  According to Lenz's law, induced effects always oppose the change i
1
 and i
2
 both are in same 
direction.  
Hence magnetic lines from B due to both currents are from right to left. By bringing A closer to B 
or increasing i
1
 right to left magnetic field from B will increase. So i
2
 should decrease. 
6.  ?
i
 = BS cos 0° = (4) (2) = 8 Wb  
  ?
f
 = BS cos 90° = 0 
   ? ?
 
= 8Wb 
    
This current is not constant. So, we cannot find the heat generated unless current function with 
time is not known. 
7.  
   
8.  If magnetic field increase than induced electric lines are anti-clockwise. If  magnetic field 
decreases, then induced electric lines are clockwise (both inside and outside the cylindrical 
region). 
On positive charge, force is in the direction of E
?
. On negative charge, force is in the opposite 
direction of E
?
.  
9.  q = 2t
2
 
    
  At t = 1s, q = 2C, i = 4A 
   
  V
c 
- V
d
 = iR = 4 × 4 = l6V  
  V
a
 - V
d
 is summation of above three i.e., 21 V. 
10.  V
a
 - V
c
 = 0 as is parallel to 
    
 
Match the Columns 
Q 1.  Match the following two columns. 
Column I Column II 
(a) Magnetic induction (p) [MT
-2
A
-1
] 
(b) Coefficient of self induction (q) [L
2
T
-2
] 
(c) LC (r) [ML
2
T
-2
A
-2
] 
(d) Magnetic flux (s) None of these 
Q 2.  In the circuit shown in figure, switch is closed at time t = 0. Match the following two columns. 
 
Column I Column II 
(a) V
L 
at t = 0 (p) zero 
(b) V
R 
at t = 0 (q) 10V 
(c) V
L 
at t = 1s 
(r) 
10
V
e
 
(d) V
R 
at t = 1s 
(s) 
1
1 10V
e
??
?
??
??
 
Q 3.  In an L-C oscillation circuit, L = 1H, 
1
CF
4
? and maximum charge in capacitor is 4 C Match the 
following two columns. Note that in column II all values are in SI units. 
Column I Column II 
(a) Maximum current in the circuit (p) 16 
(b) Maximum rate of change of current in the circuit (q) 4 
(c) Potential difference across inductor when 
q = 2C 
(r) 2 
(d) Potential difference across capacitor when rate of change of current is half its 
maximum value 
(s) 8 
Q 4.  In the circuit shown in figure, switch remains closed for long time. It is opened at time t = 0. 
Match the following two columns at t = (In 2) second. 
 
Column I Column II