Two solenoids are equal in length and radius, and the cores of both are identical cylinders of iron. However, solenoid A has four times the number of turns per unit length as solenoid B.(a) Which solenoid has the larger self-inductance?A B they are the same(b) What is the ratio of the self-inductance of solenoid A to the self-inductance of solenoid B?LA/LB =

Explanation:

= Vacuum permeability =

n = Number of turns

A = Area

I = Current

Self inductance is given by

Here, A has more turns so the self-inductance of A will be higher

For A

For B

Dividing the above two equations we have

Explanation:

Length of both the solenoids = l

Area of crossection of both the solenoids = A

Current in both the solenoids = i

Let the number of turns in coil A is 4N and the number of turns in coil B is N.

The self inductance due to the long solenoid is given by

As the current, area of crossection and the length is same so

So, LA : LB = 16 : 1

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