Question

A long solenoid has length L , average diameter D and n layer of turns .Each layer contains N turns.If current flowing through the solenoid is i the value of magnetic field at the centre :

• A. Proportional to D
• B. Inversely proportional to D
• C. Does not depend on D
• D. Proportional to L

Answer 1

The correct option is C Does not depend on D

Lets conside,

$n=$ number of layer

$N=$ number of turns

$L=$ length of long solenoid

$D=$ average diameter

$i=$ current flowing through the solenoid

The magnetic field at the centre due to long solenoid,

$B={\mu }_0{n}^{\prime }i$ (for 1 layer). . . . . . . .(1)

Where, $n^{\prime }=\frac{N}{L}$

equation (1) becomes,

$B=\frac{N}{L}{\mu }_{0}i$

For $n$ layers,

$B=\frac{nN{\mu }_{0}i}{L}$

The magnetic field at the center is independent of the average diameter.

The correct option is C.