2. Two identical conducting spheres are placed with their centers 0.30 m apart. One is given a charge of 12 x 10-9 C and the other is given a charge of - 18 x 10-9 C. a. Find the electric force exerted on one sphere by the other. b. The spheres are connected by a conducting wire. After equilibrium has occurred, find the electric force between the two spheres.

A. - 2.16 * 10^ (-5) N

B. 9 * 10^ (-7) N

Explanation:

Parameters given:

Distance between their centres, r = 0.3 m

Charge in first sphere, Q1 = 12 * 10^ (-9) C

Charge in second sphere, Q2 = - 18 * 10^ (-9) C

A. Electrostatic force exerted on one sphere by the other is:

F = (k * Q1 * Q2) / r²

F = (9 * 10^9 * 12 * 10^ (-9) * - 18 * 10^ (-9)) / 0.3²

F = - 2.16 * 10^ (-5) N

B. When they are brought in contact by a wire and are then in equilibrium, it means they have the same final charge. That means if we add the charges of both spheres and divided by two, we'll have the final charge of each sphere:

Q1 + Q2 = 12 * 10^ (-9) + (-18 * 10^ (-9))

= - 6 * 10^ (-9) C

Dividing by two, we have that each sphere has a charge of - 3 * 10^ (-9) C

Hence the electrostatic force between them is:

F = [9 * 10^9 * (-3 * 10^ (-9)) * (-3 * 10^ (-9) ] / 0.3²

F = 9 * 10^ (-7) N