Question

A ring of radius $R$ is having two charges $q$ and $2q$ distributed on its two half parts. The electric potential at a point on its axis at a distance of $2\sqrt{2}R$ from its centre is $(k=\frac{1}{4\pi {ϵ}_0})$

• A. $\frac{3kq}{R}$
• B. $\frac{kq}{3R}$
• C. $\sqrt{2}{r}_p$
• D. $\frac{3kq}{\sqrt{3}R}$

Answer 1

The correct option is C $\sqrt{2}{r}_p$

$\frac{1}{2}m{v}_p^2=\frac{1}{2}2m{v}_p^2$
$\frac{m{v}^2}{r}=qvB$
$r=\frac{mv}{qB}$
$\frac{r_o}{r_p}=\frac{2m}{m}\cdot \frac{\frac{v_p}{\sqrt{2}}}{v_p}$
$r_D=\sqrt{2}{r}_p$