Question

The centers of two identical small conducting spheres are $1m$ apart. They carry charges of opposite kind and attract each other with a force $F$ . when they are connected by a conducting thin wire they repel each other with a force $F/3$. What is the ratio of magnitude of charges carried by the spheres initially?

• A. $1:1$
• B. $2:1$
• C. $3:1$
• D. $4:1$

Answer 1

The correct option is C $3:1$

The conducting sphere $=1m$, Force $=F$ (Attraction)

when they repel $=\frac{F}{3}$

ratio of magnitude of charges carried by the sphere initially =

$F=\frac{q_1^2}{r^2}$ ($r=1m$)

$F^1=\frac{q_2}{r^2}$

$\Rightarrow \frac{F}{3}=\frac{q_2^2}{r^2}$

Now, $\frac{q_1}{q_2}=\frac{F}{F^1}=\frac{F}{F/3}=\frac{3}{1}$

or, $q_1:q_2=3:1$