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 0.155 N when their center-to-center separation is 45.4 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 0.0386 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 positive and negative charge be q1 and -q2

r = 45.4 cm = 0.454 m

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

0.155 = 9 * 10^9 * q1 * q2 /0.454^2 ...(1)

and

when they are connected with conducting wire

the new charge , q = (q1 - q2)/2

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

0.0386 = 9 * 10^9 * ((q1 - q2)/2)^2 /0.454^2 ....(2)

from (1) and (2)

q1 = 3.05 * 10^-6 C

q2 = 1.17 * 10^-6 C

a)

the negative charge is - 1.17 * 10^-6 C

b)

the positive charge is 3.05 * 10^-6 C

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