Question

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

• A. $0.6mV$
• B. $60mV$
• C. $40.2mV$
• D. $0.48mV$

Answer 1

The correct option is C $40.2mV$

$emf=-\frac{\mu N_1{N}_2}{l}\frac{\Delta I}{\Delta t}$

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

$N_1=2000$

$N_2=300$

$l=0.3m$

$\frac{\Delta I}{\Delta t}=\frac{4}{0.25}A/s$

$\Rightarrow \left|emf\right|=\frac{4\pi \times {10}^{-7}\times 2000\times 300\times 4}{0.3\times 0.25}=$ $40.212mV$