Q. The distance at which the magnetic field on axis as compared to the magnetic field at the center of the coil carrying current $I$ and radius $R$ is $\frac{1}{8}$, would be
A) $R$
B) $\sqrt{2}R$
C) $2R$
D) $\sqrt{3}R$
Explanation
(d) $\frac{B_{A}}{B_{C}} = \left( \frac{R^{2}}{x^{2} + R^{2}} \right)^{3/2}$
$\frac{1}{8} = \left( \frac{R^{2}}{x^{2} + R^{2}} \right)^{3/2} \Rightarrow \frac{1}{4} = \frac{R^{2}}{x^{2} + R^{2}}$
$\Rightarrow x^{2} + R^{2} = 4R^{2}$
$\Rightarrow x = \sqrt{3}R$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.