Q 15. We have an air-cored solenoid having a length of 30 cm, whose area is 25 cm2, and the number of turns is 500. And the solenoid has carried a current of 2.5 A. Suddenly the current is turned off and the time is taken for it is 10-3 s. What would be the average value of the induced back-emf by the ends of the open switch in the circuit? (Neglect the variation in the magnetic fields near the ends of the solenoid.)
Length of the solenoid, I = 30 cm = 0.3 mm
Area of cross-section, A=25cm2=25×10−4m2
Number of turns on the solenoid, N = 500
Current in the solenoid, I = 2.5A
Current flows for time, t = 10−3 s
Average back emf, e=d∅dt ...(1)
Where, dΦ = Change in flux = NAB ...(2)
B= Magnetic field strength =μ0NIl ...(3)
Where, μ0 = Permeability of free space =4π×10−7TmA−1
Using equations (2) and (3) in equation (1), we get
Using equations (2) and (3) in equation (1), we get
e=μ0N2IAlt=4π×10−7×(500)2×2.5×25×10−40.3×10−3=6.5V
Hence, the average back emf induced in the solenoid is 6.5 V.
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