Consider an ideal solenoid of length L, N windings, and radius b (L is much longer than b). A current I is flowing through the wire windings. If the radius of the solenoid is doubled to 2b, but all
The other quantities remain the same, the magnetic field inside the solenoid will
A) become one-half as strong as initially.
B) remain the same.
C) become one-fourth as strong as initially.
D) become twice as strong as initially.
E) become four times as strong as initially.

Question

Quizplus · Accepted Answer

The magnetic field inside an ideal solenoid is given by $B = \mu_0 \frac{N}{L} I$, where $\mu_0$ is the permeability of free space, $N$ is the number of turns, $L$ is the length of the solenoid, and $I$ is the current. This formula shows that the magnetic field inside the solenoid depends on the current and the number of turns per unit length, but not on the radius of the solenoid. Therefore, doubling the radius of the solenoid does not affect the magnetic field strength inside it.

Consider an Ideal Solenoid of Length L, N Windings, and Radius