Question

An ideal solenoid of cross-sectional area ${10}^{-4}{m}^2$ has $500$ turns per metre. At the centre of this solenoid, another coil of $100$ turns is wrapped closely around it, if the current in the coil charges from $0$ to $2A$ in $3.14ms$, the emf developed in the second coil is:

• A. $1mV$
• B. $2mV$
• C. $3mV$
• D. $4mV$

Answer 1

The correct option is D $4mV$

Mutual inductance $M=\frac{{\mu }_0\times N_1\times N_2\times A}{l}$

Emf$=M\frac{di}{dt}$

Emf$=\frac{4\pi \times 500\times 100\times {10}^{-4}}{1}\frac{2}{3.14\times {10}^{-3}}$=$4mV$