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An air cored solenoid of length 50 cm an...

An air cored solenoid of length 50 cm and area of cross section `20 m^(2)` has 200 turns and carries a current of 5.0 A. On switching off, the current decreases to across the ends of the solenoid.

Text Solution

Verified by Experts

Here, `l = 50 cm = (1)/(2) m`,
`A = 285 cm^(2) = 28 xx 10^(-4) m^(2)`
`N = 200, I = 5.0 A`,
`t = 0.1 ms = 10^(-4) s, e = ?`
`B = (mu_(0) NI)/(l) , phi_(1) = NBA = (N (mu_(0) NI))/(l) = A`
`= (mu_(0) N^(2) I A)/(l)`
`phi_(1) = (4 pi 10^(-7) (200)^(2) xx 5.0 xx 28 xx 10^(-4))/(1//2)`
`= 1.406 xx 10^(-3)` Now , `phi_(2) = 0`,
`|e| = (phi_(2) - phi_(2))/(t) = (0 - 1.406 xx 10^(-3))/(10^(-3)) = 1.4 V`
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Knowledge Check

  • An air-cored solenoid with length 30 cm, area of cross-section 25 cm^(2) and number of turns 800, carries a current of 2.5A The current is suddenly switched off in a brief time of 10^(-3)s . Ignoring the variation in magnetic field near the ends of the solenoid, the average back emf induced across the ends of the open switch in the circuit would be:

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