Question

A point charge q of mass m is located at the center of a ring having radius R and charge Q.When it is displaced slightly, the point charge accelerates along the x-axis to infinity, the ultimate speed of the point charge:-

• A. $\sqrt{\frac{2KQq}{mR}}$
• B. $\sqrt{\frac{KQq}{mR}}$
• C. $\sqrt{\frac{KQq}{2mR}}$
• D. zero

Answer 1

The correct option is A $\sqrt{\frac{2KQq}{mR}}$

Charge $=q$

mass $=m$

radius $=R$

charge $=Q$

$V=?$ (velocity)

As we know,

$U=\frac{1}{2}{mV}^2=\frac{K_{q}Q}{R}$

$\frac{1}{2}{mV}^2=\frac{K_{q}Q}{R}$

${mV}^2=\frac{2K_{q}Q}{R}$

Therefore,

$V=\sqrt{\frac{{2K}_{q}Q}{R_m}}$