Question

A ring of radius r carries a charge Q, uniformly distributed along its circumference. What is the ratio of the electric field strength at a distance R to that at a distance $\frac{R}{\sqrt{2}}$ along the axis?

• A. $\frac{\sqrt{3}}{8}$
• B. $\frac{3\sqrt{3}}{8}$
• C. $\frac{3\sqrt{3}}{4\sqrt{2}}$
• D. $\frac{2\sqrt{2}}{3\sqrt{3}}$

Answer 1

The correct option is C

$\frac{3\sqrt{3}}{4\sqrt{2}}$

E(at axis) = $\frac{K{Q}^{2}x}{(R^2+x^2{)}^{\frac{3}{2}}}$

E(at R) $=\frac{KQ}{2\sqrt{2}{R}^2}\&E\left(at\frac{R}{\sqrt{2}}\right)=\frac{2KQ}{3\sqrt{3}{R}^2}$