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

Question

5.

Two identical conducting spheres, fixed in place, attract each other with an electrostatic force of -0.5329 N when separated by 50 cm, center-to-center. 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 0.0864 N. What were the initial charges on the spheres? Since one is negative and you cannot tell which is positive or negative, there are two solutions. Take the absolute value of the charges and enter the smaller value here.

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Enter the larger value here.

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Explanation / Answer

given,

initial force = -0.5329 N

distance = 50 cm

final force = 0.0864 N

let the charges are q1 and q2 so,

force between two charges particles = kq1*q2 / d^2

for initial force

k * q1 * q2 / 0.5^2 = -0.5329

after connecting spheres with wires let the charge on each aphere becomes q because the spheres are identical so charge will distribute equally

for final force,

k * q * q / 0.5^2 = 0.0864

also the charge will ramain constant in this process so,

initial charge = final charge

q1 + q2 = 2q

on solving these equations we'll get

q1 = -5.697 * 10^-6 C

q2 = 2.598* 10^-6 C

q = -1.549 * 10^-6 C

so,

the smallest absolute value = 1.549 * 10^-6 C

the largest absolute value = 5.697 * 10^-6 C

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