Question

A small ball having charge q is suspended from a weightless, inextensible string. It is placed in a region of uniform electric field $E=3\times {10}^{4}N{m}^{-1}$ as shown in figure. In equilibrium, the string is making an angle of ${30}^0$ with the vertical. If the mass of the ball is $3\sqrt{3}$ gm, the charge on it is : $(g=10m{s}^{-2})$

• A. $+\frac{\sqrt{3}}{2}\mu C$
• B. $-\frac{\sqrt{3}}{2}\mu C$
• C. $+1\mu C$
• D. $-1\mu$C

Answer 1

The correct option is C $+1\mu C$

Let the charge on the particle be $q$.

The weight acts vertically downwards, electric force acts along the horizontal and tension along the length of the string.

Thus, we have $mg=T\cos {30}^{\circ }$ and $qE=T\sin {30}^{\circ }$

Thus, $\tan {30}^{\circ }=\frac{qE}{mg}\Rightarrow q=\frac{mg}{\sqrt{3}E}$

Given that, $m=3\sqrt{3}\times {10}^{-3}\text{kg}$ and $g=10{\text{m/s}}^2$ and $E=300\text{N/C}$

Thus, $q=\frac{3\sqrt{3}\times {10}^{-2}}{\sqrt{3}\times 300}=1\times {10}^{-4}\text{C}$