Question

A long solenoid has a radius and length of 2.30 cm and 25 cm respectively, has 580 turns. If the current in the solenoid is increasing at the rate of 17.8 A/s, what is the magnitude of the induced emf produced.

Answer 1

Induced emf is equal to 0.05 volt

Step-by-step explanation:

We have given length of the solenoid l = 25 cm = 0.25 m

Radius of the solenoid r = 2.3 cm = 0.023 m

Area of the solenoid
`A=\pi r^2=3.14* 0.023^2=0.00166m^2`

Number of turns N = 580

Inductance of the solenoid
`L=(\mu _0N^2A)/(l)=(4\pi * 10^(-7* 580^2* 0.00166))/(0.25)=0.0028H`

Rate of change of current
`(di)/(dt)=17.8A/sec`

Induced emf in inductor is equal to
`e=L(di)/(dt)=0.0028* 17.8=0.05volt`