An air cored solenoid with length 20cm, area of cross section 20cm² and number of turns 400 carries a current 2A. The current is suddenly switched off within 10^-3s,. The average back emf induced across the ends of the open switch in the circuit is (ignore the variation in magnetic field near the ends of the solenoid)

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answer is 4.

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Detailed Solution

Here, $l = 20 cm = 20 \times 10^{- 2} m$
$\begin{array}{l} A = 20 {cm}^{2} = 20 \times 10^{- 4} m^{2} \\ N = 400, I_{1} = 2 A, I_{2} = 0, dt = 10 \\ As ε = \frac{dϕ}{dt} = \frac{d (BAN)}{dt} = \frac{μ_{0} NdlAN}{ldt} (∵ B = \frac{μ_{0} NI}{t}) \\ = \frac{μ_{0} N (I_{1} - I_{2}) AN}{ldt} = \frac{4 π \times 10^{- 7} \times (400)^{2} \times 2 \times 20 \times 10^{- 4}}{20 \times 10^{2} \times 10^{- 3}} = 4 V \end{array}$

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