Question

A solenoid of radius 1.5 cm has 640 turns and a length of 25 cm.
(a) Find its inductance.
(b) Find the rate at which current must change through it to produce an emf of 80 mV.

Answer 1

Concepts and reason

The concept used to solve this problem is inductance.

Initially, the value of the inductance can be calculated by using the relation for the inductance for a solenoid. Later, the rate of change of current can be calculated by using the relation between the induced emf and the inductance of the coil.

Fundamentals

The expression for the inductance of the solenoid is,

Here, is the inductance of the coil, is the permeability of free space, is the number of turns of the coil, is the length of the coil and is the area of the coil.

The expression for the area is,

Here, is the radius of the solenoid.

The expression for the rate of change of current is,

Here, is the rate of change of current, is the induced emf, and is the inductance.

(a)

The expression for the inductance of the solenoid is,

Use for in the above equation.

Substitute for, for , for and for .

(b)

The expression for the rate of change of current is,

Substitute for and for .

Ans: Part a

The inductance of the coil is.

Part b

The rate of change of current is.