Question

Charges on two spheres are $+10\mu C$ and $-5\mu C$ respectively. They experience a force $F$. If each of them is given an additional charge $+2\mu C$ then new force between them keeping the same distance is

• A. $18F$
• B. $\frac{F}{25}$
• C. $\frac{18F}{25}$
• D. $\frac{25}{18}F$

Answer 1

Answer: (C)

When there is no additional charge
$F=\frac{K(+10)(-5)}{R^2}$
$F=\frac{-50K}{R^2}$...(i)
when $+2\mu C$ charge is added to both spheres.
Charge on $1^{\text{st }}$ sphere $=10\mu C+2\mu C=12\mu C$
Charge on $2^{\text{nd }}$ sphere $=-5\mu C+2\mu C=-3\mu C$
New force will be $F^{\prime }=\frac{K(+12)(-3)}{R^2}=-\frac{36K}{R^2}$...(ii)
From (i) and (ii)
$\therefore \frac{F^{\prime }}{F}=-\frac{36K}{R^2}\times \frac{R^2}{-50K}$
$=\frac{36}{50}$
$\Rightarrow \frac{F}{F}=\frac{18}{25}$