Question

A metal sphere, X, has an initial net charge of −6 × 10−6 coulomb and an identical sphere, Y, has an initial net charge of +2 × 10−6 coulomb. The spheres touch each other and then separate. What is the net charge on sphere X after the spheres have separated?

Answer 1

When the two spheres touch each other, part of the charge recombine together. The part of charge that recombines is the excess of positive charge on sphere Y, $Q_y = +2 \cdot 10^{-6}C$, that recombines with an equivalent charge of $-2 \cdot 10^{-6}C$ located on sphere X. As a result, the total charge remained on the two spheres is the excess of negative charge remained on sphere X:
$Q=-4 \cdot 10^{-6}C$
Since the two spheres are identical, they have same capacity, so this charge will now redistribute equally on the two spheres: therefore, at the end, each sphere will have
$\frac{Q}{2}=-2 \cdot 10^{-6} C$