Question

Two identical conducting spheres, fixed in place, attract each other with an electrostatic force of 0.116 N when their center-to-center separation is 65.4 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 0.0273 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

Part a)

`q_1 = -1.47 * 10^(-6) C`

Part b)

`q_2 = 3.75 * 10^(-6) C`

Step-by-step explanation:

Let the charge on two spheres is q1 and q2

now the force between two charges are

`F = (kq_1q_2)/(r^2)`

`0.116 = ((9* 10^9)(q_1)(q_2))/(0.654^2)`

`q_1 q_2 = 5.51 * 10^(-12)`

now when we connect then with conducting wire then both sphere will equally divide the charge

so we will have

`q = (q_1-q_2)/(2)`

now we have

`0.0273 = ((9* 10^9)((q_1- q_2)/(2))^2)/(0.654^2)`

`q_1 - q_2 = 2.28* 10^(-6) C`

now we will have

Now we can solve above two equations

Part a)

negative charge on the sphere is

`q_1 = -1.47 * 10^(-6) C`

Part b)

positive charge on the sphere is

`q_2 = 3.75 * 10^(-6) C`