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 0.125 N when their center-to-center separation is 50.4 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 0.0470 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,

sepration , r = 50.4 cm = 0.504 m

let the two charges be q1 and - q2

the electrostatic force , F1= K * q1 * q2 /r^2

0.125 = 9 * 20^9 * q1 * q2 /0.504^2 ...(1)

when they are connected with a conducting wire

the charge on each sphere , q = ( q1 - q2)/2

the electrostatic force , F2 = K * q^2 /r^2

0.047 = 9 * 10^9 * q^2 /0.504^2

0.047 = 9 * 10^9 * ((q1 - q2)/2)^2 /0.504^2 ...(2)

from (1) and (2)

q1 = 3 * 10^-9 C

q2 = 2.31 * 10^-9 C

a)

the negative charge is - 2.31 * 10^-9 C

b)

the positive charge is 3 * 10^-9 C

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