Question

A solenoid of radius 2.3 cm has 370 turns and a length of 25 cm.
(a) Find its inductance.
___ mH
(b) Find the rate at which current must change through it to produce an emf of 73 mV.
___ A/s

Answer 1

Concepts and reason

The concepts used to solve these problems are the inductance of solenoid and the voltage of the solenoid.

Use the relationship between the number of turns, area of cross-section, the length and the inductance to calculate the inductance.

Then, using the relationship between the voltages, the inductance and the rate at which the current change, find the rate at which the current must change.

Fundamentals

The expression for the inductance of solenoid is as follows:

Here, the induction is , the number of turns in solenoid is , the cross-sectional area of solenoid is , the length of the solenoid is , and the relative permeability is .

The expression for the voltage in solenoid is as follows:

$1=1 $

Here, the voltage is , inductance is , and the rate of change of current with respect to time is .

(a)

The expression for the area of the solenoid is as follows:

Here, the radius of solenoid is .

Substitute for .

The expression for the inductance of solenoid is as follows:

Substitute for , for , for , and for .

(b)

The expression for the voltage in solenoid is as follows:

$1=1 $

Rearrange the equation to get the expression for the rate of change of current.

Substitute for and for .

The rate of change of current is as follows:

Ans: Part a

The inductance of the solenoid is .

Part b

Thus, the rate at which the current must change through the solenoid to produce an emf of is .