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NCERT Class XII Chapter
Electromagnetic Induction
Questions With Solutions

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Question : 3
Total: 17
A long solenoid with 15 turns per cm has a small loop of area 2.0 cm2 placed inside the solenoid normal to its axis. If the current carried by the solenoid changes steadily from 2.0 A to 4.0 A in 0.1 s, what is the induced emf in the loop while the current is changing?
Solution:  
When the current changes through the solenoid, a change in magnetic field also take place within it.
Initial magnetic field in solenoid,
B1 = µ0nI1 = 4π × 10−7 ×
15
10−2
 × 2 = 120π × 10−5 T
Final magnetic field , B2 = µ0nI2
B2 = 4π × 10−7 ×
15
10−2
 × 4 = 240π × 10−5 T
Initial flux through coil inside solenoid placed normal to axis.
ϕi = B1A = 120π × 10−5 × 2 × 10−4
ϕi = 240π × 10−9 Wb
Final flux, ϕf = B2A = 240π × 10−5 × 2 × 10−4
ϕf = 480π × 10−9 Wb
Induced emf
ε = −
(ϕf−ϕi)
t
 = −
240×10−9×3.14
0.1
 = - 7.5 µV
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