Question

An air-cored solenoid with length 30 cm, area of cross-section 25 cm2 and number of turns 800, carries a current of 2.5 A. The current is suddenly switched off in a brief time of 10^-3s. Ignoring the variation in magnetic field near the ends of the solenoid, the average back emf induced across the ends of the open switch in the circuit would be ______.

Options

• zero

• 3.125 volts

• 6.54 volts

• 16.74 volts

Answer 1

An air-cored solenoid with length 30 cm, area of cross-section 25 cm2 and number of turns 800, carries a current of 2.5 A. The current is suddenly switched off in a brief time of 10^-3s. Ignoring the variation in magnetic field near the ends of the solenoid, the average back emf induced across the ends of the open switch in the circuit would be 16.74 volts.

Explanation:

Magnetic field inside a solenoid

B = `mu_0 "N"/l`I'

Flux linked with ‘N’ turns

Initial flux  `phi_1 = "NBA" = "N" mu_0 "N"/l "IA"`

= `mu_0 "N"/l "IA"`

= `(4pi xx 10^-7 xx 800 xx 800 xx 2.5 xx 2.5 xx 10^-4)/0.30`

`= 16.74 xx 10^-3`Wb

Final flux `phi_2` = 0

Average back emf |e| = `("d"phi)/"dt" = (16.74 xx 10^-3 - 0)/10^-3`

= 16.74 V