Question

Two identical conducting spheres, fixed in place, attract each other with an electrostatic force of 0.149 N when their center-to-center separation is 55.0 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 0.0369 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.)

Answer 1

let the charge on the spheres be Q₁ and Q₂

Given that :

0.149 = force of attaraction between spheres

0.149 = k Q₁ Q₂/(0.55)²

0.149 = (9 x 10⁹) Q₁ Q₂/(0.55)²

Q₁ Q₂ = 5 x 10^-12

Q₁ = ( 5 x 10^-12 )/Q₂ eq-1

since the charges are opposite , hence

Q₁ Q₂ = - 5 x 10^-12

after the spheres are connected by a wire , they aquire equal charge which is given as

Q = (Q₁ + Q₂ )/2

Also

0.0369 = k Q²/r²

0.0369 = (9 x 10⁹) Q²/(0.55)²

Q = 1.1 x 10^-6

(Q₁ + Q₂ )/2 = 1.1 x 10^-6

Q₁ + Q₂ = 2.2 x 10^-6

using eq-1

(( 5 x 10^-12 )/Q₂ ) + Q₂ = 2.2 x 10^-6

Q₂ = 3.6 x 10^-6

Q₁ = 1.4 x 10^-6