Question

# Two identical conducting spheres, fixed in place, attract each other with an electrostatic force of 0.149...

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.)

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

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