P22_004.PDF

4. The fact that the spheres are identical allows us to conclude that when two spheres are in contact,

they share equal charge. Therefore, when a charged sphere ( q ) touches an uncharged one, they will

(fairly quickly) each attain half that charge ( q/ 2). We start with spheres 1 and 2 each having charge

q and experiencing a mutual repulsive force F = kq 2 /r 2 . When the neutral sphere 3 touches sphere 1,

sphere 1’s charge decreases to q/ 2. Then sphere 3 (now carrying charge q/ 2) is brought into contact

with sphere 2, a total amount of q/ 2+ q becomes shared equally between them. Therefore, the charge

of sphere 3 is 3 q/ 4 in the ﬁnal situation. The repulsive force between spheres 1 and 2 is ﬁnally

F = k 2 3 4

r 2

r 2 = 3

8 F.

8 k q 2

= 3