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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. - Physics

Numerical

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. 

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Solution

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

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