Question

A circular solenoid has 100 loops per centimeter, a radius of 4.53 cm, a length of 8.88 cm, and carries a current of 500 mA. It's inductance is:____________

a) 7.75 mH
b) 71.9 mH
c) 18.0 mH
d) 0.912 mH

Answer 1

The inductance of the solenoid is 71.98 mH

Step-by-step explanation:

Given;

number of loops per length of the solenoid, n = 100 loops/cm

radius of the solenoid, r = 4.53 cm

length of the solenoid, L = 8.88 cm

current carried by the solenoid, I = 500 mA

The inductance of the solenoid is calculated as;

`L = (N^2* \mu_0 * A)/(l)`

where;

A is the area of the coil

`A =\pi r^2 = \pi (0.0453)2 = 0.00645 \ m^2`

N is the number of turns, = 100 x 8.88 = 888 loops

l is the length = 0.0888 m

`L = (N^2* \mu_0 * A)/(l)\\\\L = ((888)^2* \(4\pi * 10^(-7)) * (0.00645))/(0.0888)\\\\L = 0.07198 \ H\\\\L = 71.98 \ mH`

Therefore, the inductance of the solenoid is 71.98 mH