Numerical

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

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#### Solution

l = 0. 5m

n = 10 turns /cm = 10 × 10^{+2} turns/ m

a = 1 cm^{2} = 10^{-4}

`(di)/(dt) = (2-1)/0.1 = 1/(0.1) = 10 `A / s

`ε = -L (di)/(dt)`

` = mu_0 n^2 Al (di)/(dt)`

= 4π × 10^{-7} × (10^{+3})^{2} × 10^{-4} × 0.5 × 10

= 4π × 10^{-7} × 10^{6} × 10^{-4} × 5 × 10^{-1 }× 10

ε = 20π × 10^{-5} V

Concept: Faraday’s Law of Induction

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