Question

A solenoid of radius 3.5 cm has 800 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 90 mV. (Enter the magnitude.)
A/s

Answer 1

a)

The magnetic flux is produced by the solenoid is given by

the magnetic flux through a single turn is given by

In a length 'l', there are 'nl' such turns, so the total flux is given by

we know that from the definition of the inductance

where

n=no of turns

l=length of solenoid

R=radius of solenoid

I=current through the solenoid

L=inductance of the solenoid

comparing equation (1) and equation (2) we get

Given

n=800

l=25cm=0.25m

R=3.5cm=0.35m

so

or,

b)

the emf is given by

or,

or,

the rate of change of current is

Given,

so,