Class 12 Physics
CBSE and UP Board
Electromagnetic Induction
Chapter-6 Exercise 6.3
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?
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Number of turns on the solenoid = 15 turns/cm = 1500 turns/m
Number of turns per unit length, n = 1500 turns
The solenoid has a small loop of area, A = 2.0 cm2 = 2 x 10⁻4 m2
Current carried by the solenoid changes from 2 A to 4 A.
Therefore, change in current in the solenoid, di = 4- 2 = 2A
Change in time, dt = 0.1 s
Induced emf in the solenoid is given by Faraday’s law as: e =dφ/dt ————Eq-1
Where, φ= Induced flux through the small loop =BA————–Eq -2 B = Magnetic field =μ0ni————–Eq -3
μ0 = Permeability of free space = 4π x10-7 H/m
Hence, equation (i) reduces to:
e =d/dt (BA)
= Aμ0n (di/dt)
= 2 x 10⁻4 x 4π x10-7 x 1500 x 2/ 0.1
= 7.54 x 10⁻⁶ V
Hence, the induced voltage in the loop is 7.54 x 10-6V