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

Answer:

Induced emf is equal to 0.05 volt

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 $A=\pi r^2=3.14\times 0.023^2=0.00166m^2$

Number of turns N = 580

Inductance of the solenoid $L=\frac{\mu _0N^2A}{l}=\frac{4\pi \times 10^{-7\times 580^2\times 0.00166}}{0.25}=0.0028H$

Rate of change of current $\frac{di}{dt}=17.8A/sec$

Induced emf in inductor  is equal to $e=L\frac{di}{dt}=0.0028\times 17.8=0.05volt$