Question

An air cored solenoid with length 20 cm, area of cross section 20 cm2 and number of turns 400 carries a current 2 A. The current is suddenly switched off within 10-3 s. The average back emf induced across the ends of the open switch in the circuit is (ignore the variation in magnetic field near the ends of the solenoid)

• A. 2 V
• B. 4 V
• C. 3 V
• D. 5 V

Answer 1

Answer: (B)

4 V

Answer 2

Here $l = 20cm = 20 \times 10^{- 2}m,$

$A = 20cm^{2} = 20 \times 10^{- 4}m^{2}$

$N = 400,I_{1} = 2A,I_{2} = 0,dt = 10^{- 3}s$

As $\varepsilon = \frac{d\varphi}{dt} = \frac{d(BAN)}{dt}$

$= \frac{\mu_{0}NdIAN}{ldt}$ $\left( \because B = \frac{\mu_{0}NI}{l} \right)$

$= \frac{\mu_{0}N(I_{1} - I_{2})AN}{ldt}$

$= \frac{4\pi \times 10^{- 7} \times (400)^{2} \times 2 \times 20 \times 10^{- 4}}{20 \times 10^{- 2} \times 10^{- 3}} = 4V$