Two identical conducting spheres, fixed in place, attract each other with an ele

Question

Two identical conducting spheres, fixed in place, attract each other with an electrostatic force of 0.0859 N when their center-to-center separation is 63.3 cm. The spheres are then connected by a thin conducting wire. When the wire is removed, the spheres repel each other with an electrostatic force of 0.0297 N. Of the initial charges on the spheres, with a positive net charge, what was (a) the negative charge on one of them and (b) the positive charge on the other? (Assume the negative charge has smaller magnitude.)

Explanation / Answer

here,

let the charges be -q and Q

distance between the charges , d = 63.3 cm

d = 0.633 m

force between the charges , F = K * q *Q/d^2

0.0859 = 9 * 10^9 * q * Q /0.633^2 ...(1)

when the charges are connected by conducting wire ,

let the charge on each sphere when removes be q' = (Q-q)/2 ...(2)

electrostatic force , F = k * (q')^2 / d^2

0.0297 = 9 * 10^9 * ((Q-q)/2)^2 /0.633^2 ....(3)

from equation (1) and (3)

q = 1.12 * 10^-6 C

Q = 3.41 * 10^-6 C

(a)

the negative charge on one of them is - 1.12 * 10^-6 C

(b)

the positive charge on one of them is 3.41 * 10^-6 C

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