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 0.0977 N when their center-to-center separation is 40.0 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 0.0480 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 charge on spheres be q1 and (-q2)

sepration between spheres , d = 0.4 m

initially force between the charges , F = k * q1 * q2 /d^2

0.0977 = 9 * 10^9 * q1 * q2 /( 0.4^2) ...(1)

and

after they are connected by a thin wire , the charge on each sphere , q = ( q1 - q2)/2

electric force = 0.048 N

k * q^2 /d^2 = 0.048

9 * 10^9 * (q1 - q2)^2 /( 4 * 0.4^2) = 0.048 ...(2)

from (1) and (2)

q1 = 2.53 * 10^-6 C , q2 = 6.86 * 10^-7 C

the positive charge is 2.53 * 10^-6 C

the magnitude of negative charge is 6.86 * 10^-7 C or - 6.86 * 10^-7 C

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