# An air - cored solenoid with length 30 cm, area of cross - section 25 cm2 and number of turns 500, carries a current of 2.5 A. The current is suddenly switched off in a brief time of 10–3 s. How much is the average back emf induced across the ends of the open switch in the circuit? Ignore the variation in magnetic field near the ends of the solenoid.

Given: Length of the solenoid = 30 cm=0.30 m

Area of cross - section = 25 cm2 = 25m× 10-4m-2

No. of turns in the solenoid = 500

Current, i = 2.5A

Time for which the current flows t = 10–3 s

The average back emf induced across the ends of the open switch in the circuit is as follows: ………………(i)

where dФ is the change in the flux and is equal to NAB

B is the magnetic field = (μ0Ni)/l

Substituting in equation (i), we get Substituting the values in above equation , we get On solving, we get

e = 6.5 V

the emf induced in the solenoid is 6.5V

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