Question

A long solenoid with 10 turns per cm has a small loop of area 3 cm2 placed inside, normal to the axis of the solenoid. If the current carried by the solenoid changes steadily from 2 A to 4 A in 0.2 s, what is the induced voltage in the loop, while the current is changing?

• A. 4.2 × 10-8 V
• B. 2.8 × 10-8 V
• C. 7.3 × 10-6 V
• D. 3.8 × 10-6 V

Answer 1

Answer: (D)

3.8 × 10-6 V

Answer 2

Here , $\frac{N}{l} = 10$ turns per cm = 1000 turns per m

$A = 3cm^{2} = 3 \times 10^{- 4}m^{2}or\frac{DI}{dt} = \frac{4 - 2}{0.2} = 10As^{- 1}$

Also $\varepsilon = \frac{d\varphi}{dt} = \frac{d}{dt}(BA) = A\frac{d}{dt}\left( \mu_{0}\frac{N}{l}I \right)$

$= A\mu_{0}\left( \frac{N}{l} \right)\frac{dI}{dt}$

$= 3 \times 10^{- 4} \times 4\pi \times 10^{- 7} \times 1000 \times 10$

$= 3.8 \times 10^{- 6}V$