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 0.6286 N when their center-to-center separation is 50 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 0.2525 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.

Explanation / Answer

let initial charges be q1 and q2 with q2 being the -ve and smaller of the two

then 9*10^9*q1*q2/0.5^2=0.7926

q1*q2=2.2*10^(-11)

after being connected by thin wire,

their charges will become same as they are identical(so same capacitance,and as they are connected same potential,so charge=capacitance*potential,so same charge)

let new charge on each of them be q.

then 9*10^9*q^2/0.5^2=0.1896

q=2.3 uC

so (q1-q2)/2=2.3 uC

q1-q2=4.6 uC

solving eqn(1) and eqn(2),

we get

q1=2.92 uC

then q2=-1.68 uC

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