Question

A solenoid has $2000$ turns wound over a length of $0.3m$. The area of its cross-section is $1.2\times {10}^{-3}{m}^2$. Around its central portion, a coil of $300$ turns is wound. If an initial current of $2A$ in the solenoid is reversed in $0.25s$, the e.m.f. induced in the coil is equal to:

• A. $48mV$
• B. $48kV$
• C. $6\times {10}^{-4}V$
• D. $6\times {10}^{-2}V$

Answer 1

The correct option is A $48mV$

The mutual inductance between two coil is $M=\frac{{\mu }_0{N}_1{N}_{2}A}{L}$

Induce emf , $\epsilon =M\frac{dI}{dt}=\frac{{\mu }_0{N}_1{N}_{2}A}{L}\frac{dI}{dt}$

or $\epsilon =\frac{4\pi \times {10}^{-7}\times 2000\times 300\times (1.2\times {10}^{-3})}{0.3}\times \frac{2-(-2)}{0.25}=0.048V=48mV$