Question

A .0.5m long solenoid of 10 turns/cm has area of cross-section 1cm² . Calculate the voltage induced across  its ends if the current in the solenoid is changed from 1A to 2A in 0.1s. 

Answer 1

l = 0. 5m 

n = 10 turns /cm = 10 × 10⁺² turns/ m 

a = 1 cm² = 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 × 10⁶ ×  10^-4 × 5 × 10^-1 × 10

       ε =   20π × 10^-5 V