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Question

Consider a long solenoid that has length L, average diameter D, and n layer of turns. Each layer contains N turns. If the current flowing through the solenoid is I the value of the magnetic field at the center:


  1. Does not depend on D

  2. Proportional to L

  3. Proportional to D

  4. Inversely Proportional to 2D

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Solution

The correct option is A

Does not depend on D


Step 1: Let's consider

n is the number of layers.

N is the number of turns.

L is the length of a long solenoid.

D is the average diameter.

I is the current flowing.

Step 2: Calculation

For the first layer, the magnetic field at the center due to the long solenoid is:

B=μ0ni…(equation 1)

Here,

n'=NL

By substituting n' in the equation 1, we get

B=NLμ0i

Now, for n layers, the magnetic field be:

B=nNμ0iL

As we can see that the magnetic field at the center is independent of the average diameter.

Therefore, option A is the correct answer.


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