Question

A current in a $240$ turn solenoid varies at $0.8A/s$. Find emf induced if the length of the solenoid is $12cm$ and radius $2cm$:

• A. $6.14\times {10}^{-4}V$
• B. $6.4\times {10}^{-3}V$
• C. $3.07\times {10}^{-3}V$
• D. $3.07\times {10}^{-4}V$

Answer 1

The correct option is A $6.14\times {10}^{-4}V$

emf induced $\epsilon =L\frac{di}{dt}$
$L=\frac{{\mu }_0{N}^2\left(\pi r^2\right)}{l}$
$\epsilon =\frac{{\mu }_0{N}^2\left(\pi r^2\right)}{l}\frac{di}{dt}$
$=\frac{4\pi \times {10}^{-7}\times (240{)}^2\times (\pi \left)\right(2\times {10}^{-2}{)}^2\times 0.8}{12\times {10}^{-2}}$
$=6.14\times {10}^{-4}V$