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 0.149 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.)

Explanation / Answer

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

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.