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

Answer 1

Answer: (C)

When there is no additional charge
$F=\frac{K(+10)(-5)}{R^{2}}$
$F=\frac{-50 K}{R^{2}}$...(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 $F'=\frac{K(+12)(-3)}{R^{2}}=-\frac{36 K}{R^{2}}$...(ii)
From (i) and (ii)
$\therefore \frac{F'}{F}=-\frac{36 K}{R^{2}} \times \frac{R^{2}}{-50 K}$
$=\frac{36}{50}$
$\Rightarrow \frac{F}{F}=\frac{18}{25}$