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 Q_{1} and
Q_{2}

Given that :

0.149 = force of attaraction between spheres

0.149 = k Q_{1} Q_{2}/(0.55)^{2}

0.149 = (9 x 10^{9}) Q_{1}
Q_{2}/(0.55)^{2}

Q_{1} Q_{2} = 5 x 10^{-12}

Q_{1} = ( 5 x 10^{-12} )/Q_{2} eq-1

since the charges are opposite , hence

Q_{1} Q_{2} = - 5 x 10^{-12}

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

Q = (Q_{1} + Q_{2} )/2

Also

0.0369 = k Q^{2}/r^{2}

0.0369 = (9 x 10^{9})
Q^{2}/(0.55)^{2}

Q = 1.1 x 10^{-6}

(Q_{1} + Q_{2} )/2 = 1.1 x 10^{-6}

Q_{1} + Q_{2} = 2.2 x 10^{-6}

using eq-1

(( 5 x 10^{-12} )/Q_{2} ) + Q_{2} = 2.2
x 10^{-6}

Q_{2} = 3.6 x 10^{-6}

Q_{1} = 1.4 x 10^{-6}

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