Question

A solenoid is 20cm long and has a cross sectional area of ​​5x10 ^ -4 m2. When the current through the solenoid decreases at a rate of 0.625A / s, the induced emf is 2x10 ^ -4V. Find the number of turns / unit length of the solenoid

Answer 1

B = µ0n I

differentiate w.r.t to time we get dB/dt = µ0n dI /dt

multiply above eqaution by area both side.

A*dB/dt = A*µ0n dI /dt

we know , E = − d Φ B d t and  Φ = B.A

hence , above equation become in this way that is E = A*µ0n dI /dt

We Know E = 2x10 ^ -4V

A = ​​5x10 ^ -4 m2 ;;;; change in current w.r.t is f 0.625A / s,

putting values we get ,

2x10^-4 = ​​5x10^-4 * 0.625 * µ * n

we get n = 0.050955414 * 10 ⁷

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