Rankers Physics

Force Acting on Moving Charges: Practice Problem & Solution

An electron moves in a circular orbit with a uniform speed $v$. It produces a magnetic field $B$ at the center of the circle. The radius of the circle is proportional to: (2005)
$B/v$
$v/B$
$\sqrt{v/B}$
$\sqrt{B/v}$

Solution Explained:

To solve this problem, we apply the core principles of Force Acting on Moving Charges. Understanding the underlying formula is key to arriving at the correct answer below:

Center field is $B = \frac{\mu_0 I}{2R}$ with $I = \frac{ev}{2\pi R}$, giving $B = \frac{\mu_0 ev}{4\pi R^2}$. Thus, radius $R$ is proportional to $\sqrt{v/B}$.

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