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:
Does not depend on D
Proportional to L
Proportional to D
Inversely Proportional to 2D
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:
…(equation )
Here,
By substituting n' in the equation , we get
Now, for n layers, the magnetic field be:
As we can see that the magnetic field at the center is independent of the average diameter.
Therefore, option A is the correct answer.