Biot-Savart Law & Circular Coils question from NEET 2005 (AIPMT)

Answer: (c)

1. $I = \frac{ev}{2\pi r}$, so $B = \frac{\mu_0 I}{2r} = \frac{\mu_0 e v}{4\pi r^2}$.
2. $r^2 \propto \frac{v}{B} \Rightarrow r \propto \sqrt{v/B}$
3. So the answer is (c) $\sqrt{v/B}$.