An air cored solenoid with length 20 cm, area of cross section 20 cm2 and number of turns 400 carries a current 2 A. The current is suddenly switched off within 10-3 s. 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)

Question

An air cored solenoid with length 20 cm, area of cross section 20 cm2 and number of turns 400 carries a current 2 A. The current is suddenly switched off within 10-3 s. 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) (A) 2 V (B) 4 V (C) 3 V (D) 5 V

Tardigrade Admin · Accepted Answer

Here, l = 20 cm = 20 × 10-2 m, A=20 cm2=20×10-4 m2 N=400, I1=2 A, I2=0, dt=10-3 s As ε= (d φ/dt)=(d(BAN)/dt) =(μ0N dl AN/l dt)(∵ B=(μ0NI/t)) =(μ0N (I1-I2)AN/l dt) =( 4 π×10-7×(400)2×2×20×10-4/20×102×10-3 ) =4 V

$2 V$

$4 V$

$3 V$

$5 V$

2V

4V

3V

5V

Here, l=20cm=20×10−2m, A=20cm2=20×10−4m2 N=400, I1​=2A, I2​=0, dt=10−3s As ε=dtdϕ​=dtd(BAN)​ =ldtμ0​NdlAN​(∵B=tμ0​NI​) =ldtμ0​N(I1​−I2​)AN​ =20×102×10−34π×10−7×(400)2×2×20×10−4​ =4V

$2 V$

$4 V$

$3 V$

$5 V$