Question

Two identical metal spheres separated by a distance x are charged to $Q$ and $-2Q$ . They are brought in contact with each other and then again separated to original distance. The ratio of the magnitudes of the forces between the two spheres before and after contact is :

• A. $8:1$
• B. $1:8$
• C. $2:1$
• D. $1:2$

Answer 1

Answer: (A)

$8:1$

Initial force is given as,

$F_1=\frac{kQ\left(-2Q\right)}{R^2}$ (1)

When both charge came in contact final charge on each of them

$q=\frac{Q+\left(-2Q\right)}{2}=\frac{-Q}{2}$

Final force is given as,

$F_2=\frac{k{\left(-Q/2\right)}^2}{R^2}$ (2)

Diving first equation by second we get

$\frac{F_1}{F_2}=\frac{8}{1}$

Thus initial force will be eight times of the final force.