Metal sphere 1 has a positive charge of 7.00 nc . metal sphere 2, which is twice the diameter of sphere 1, is initially uncharged. the spheres are then connected together by a long, thin metal wire. what are the final charges on each sphere?

2.33 nC, 4.67 nC

Explanation:

when the two spheres are connected through the wire, the total charge (Q=7.00 nC) re-distribute to the two sphere in such a way that the two spheres are at same potential:

(1)

Keeping in mind the relationship between charge, voltage and capacitance:

we can re-write (1) as

(2)

where:

Q1, Q2 are the charges on the two spheres

C1, C2 are the capacitances of the two spheres

The capacitance of a sphere is given by

where R is the radius of the sphere. Substituting this into (2), we find

(3)

we also know that sphere 2 has twice the diameter of sphere 1, so the radius of sphere 2 is twice the radius of sphere 1:

So the eq.(3) becomes

And re-arranging it we find:

And since we know that the total charge is

we find