# A $0.5\; m$ long solenoid of $10\; turns/cm$ has area of cross-section $1\; cm^{2}$ . Calculate the voltage induced across its ends if the current in the solenoid is changed from $1A$ to $2A$ in $0.1s$.

The voltage induced across its ends if the current in the solenoid is changed from 1A to 2A in 0.1 s:

Induced Voltage is given as :

$\left | V \right |=L\frac{dI}{dt}$

therefore, $\left | v \right |=\mu _{0}n^{2}la\frac{dI}{dt}$

given 10 turns /cm, there for 0.5m=50 cm the number of turns N = 500

$n=\frac{N}{l}=\frac{500}{0.5}$

$\left | V \right |=4\pi 10^{-7}\times \left ( \frac{500}{0.5} \right )^{2}\times 0.5\times 1\times 10^{-4}\times \frac{(2-1)}{0.1}$

$\left | V \right |=6.28\times 10^{-4} Volt$

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