Suppose we have two separate infinite solenoids, one with twice the radius of the other, that are otherwise identical (they have the same number of turns per unit length and the current flowing in those turns is the same). How does the magnitude of the field $\left|\vec{B}_{2}\right|$ inside the solenoid with the larger radius compare to the field magnitude $\left|\vec{B}_{1}\right|$ inside the smaller solenoid?
A) $\left|\overrightarrow{B_{2}}\right|=4\left|\overrightarrow{B_{1}}\right|$
B) $\left|\overrightarrow{B_{2}}\right|=2\left|\overrightarrow{B^{\prime}}\right|$
C) $\left|\overrightarrow{B_{2}}\right|=\left|\overrightarrow{B_{1}}\right|$
D) $\left|\overrightarrow{B_{2}}\right|=1 / 2\left|\overrightarrow{B_{1}}\right|$
E) $\left|\overrightarrow{B_{2}}\right|=1 / 4\left|\overrightarrow{B_{1}}\right|$
F) Some other ratio (specify)

Question

Quizplus · Accepted Answer

The magnetic field inside an ideal solenoid is given by $B = \mu_0 n I$, where $\mu_0$ is the magnetic constant, $n$ is the number of turns per unit length, and $I$ is the current. Since both solenoids have the same $n$ and $I$, the magnetic field inside them will be the same, regardless of their radius.

Suppose We Have Two Separate Infinite Solenoids, One with Twice ∣B⃗2∣\left|\vec{B}_{2}\right|​B2​​

Suppose We Have Two Separate Infinite Solenoids, One with Twice $\left|\vec{B}_{2}\right|$