An air- conred solectioid with length 30 cm,area of cross-section `25 cm^(2)` and number of turns 500, carries a curent 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 opne switch in the circuit ? lgnore the variation inmagnetic field near the of the solenoid .

Options

A. 6.5 V
B. 7.4 V
C. 8.2 V
D. 9.3 V

Answer

A

Explanation

Given , length of solenoid l = 30 cm = `30 xx 10^(-2)` m
Area of cross-section `A = 25 cm^(2) = 25 xx 10 ^(-4)m^(2)`
Number of turns, N = 5000
Current ,`l_(1)= 21.5 A, l_(2) = 0`
Brief time `dt = 10 ^(-3) s`
Induced emf in the solenoid
`e= (dphi)/(dt)= (d)/(dt)(BA)" "[thereforephi= BA]`
Magnetic field induction B at point well inside the long solenoid carrying current l is
`B= mu_(0) nl("where, n= number of turns per unit lenght "=(N)/(l))`
`e = NA(dB)/(bt) = A(d)/(dt)(mu_(0)(N)/(l))= A (mu_(0)N)/(l).(dl)/(dt)`
`e = 500 xx 25 xx 10^(-4) xx 4 xx 3.14 xx 10 ^(-7)xx(500)/(30 xx 10^(-2))xx(2.5)/(10^(-3))`