Question

A small sphere with mass 1.2 g hangs by a thread between two parallel vertical plates 5.00 cm apart. The plates are insulating and have uniform surface charge densities $+\sigma$ and $-\sigma$. The charge on the sphere is $q=9\times {10}^{-6}C$. What potential difference between the plates will cause the thread to assume an angle of ${37}^{\circ }$ with the vertical as shown in figure ?

• A. $30V$
• B. $12V$
• C. $50V$
• D. $25V$

Answer 1

The correct option is C $50V$

$q=9\times {10}^{-6}C,m=1.2ℊ=\frac{1.2}{1000}㎏$
$d=5㎝=\frac{5}{100}m,\theta =37°$
Electric field, $E=\frac{V}{0.05}$
Force, $F=qE=q\frac{V}{0.05}$
$\Rightarrow mg\cos \theta =q\times \frac{V}{0.05}$
$\Rightarrow V=\frac{0.05\times mg\cos \theta }{q}$
$=\frac{0.05\times 1.2\times {10}^{-3}\times 10\times \cos 37°}{9\times {10}^{-6}}$
$\simeq 50V$