Question

Two identical conducting spheres, one having an initial charge +Q and the other initially uncharged, are brought into contact.

1. What is the new charge on each sphere?

2. While the spheres are in contact, a positively charged rod is moved close to one sphere, causing a redistribution of charges on the two spheres, so the charge on the sphere closest to the rod has a charge - Q. What is the charge in the other sphere?

Answer 1

When the sphere are brought into contactthey become equipotential.

$\frac{q_1}{4\pi \epsilon r}=\frac{q_2}{4\pi r\epsilon }$

$q_1=q_2.............\left(1\right)$

But, from conservation of charge,

$q_1+q_2=Q$

Fom eq(1) and eq(2)

$2q_1=Q⟹q_1=\frac{Q}{2}=q_2$

Net induced charge is always is zero,

Hence net charge on two sphere remains unchanged

$-Q+Q^{\prime }=Q$

$2Q=Q$ '

Hence, +2Q will be charge on second sphere.