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 chargeq and experiencing a mutual repulsive force F = kq2/r2. When the neutral sphere 3 touches sphere 1,sphere 1s charge decreases to q/2. Then sphere 3 (now carrying charge q/2) is brought into contactwith sphere 2, a total amount of q/2 + q becomes shared equally between them. Therefore, the chargeof sphere 3 is 3q/4 in the nal situation. The repulsive force between spheres 1 and 2 is nally

F = k

(q2

) ( 3q4

)

r2=

38kq2

r2=

38F .

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