Question

A metal ball with diameter of a half a centimeter and hanging from an insulating thread is charged up with 1010 excess electrons. an initially uncharged identical metal ball hanging from an insulating thread is brought in contact with the first ball, then moved away, and they hang so that the distance between their centers is 20 cm. (a) calculate the electric force one ball exerts on the other, and state whether it is attractive or repulsive. (enter the magnitude of the force.)

Answer 1

When the metals touch together, half the charge of the charged metal flows to the other because the electrons all repel each other. Therefore this also means that each metal ball contains the same amount of electrons. Each ball has 5^10 electrons, this is equivalent to a total charge of:

Q1 = Q2 = (1.602 * 10^-19 coulombs / electron) 5^10 electrons = Q

Q = 1.564 * 10^-12 C

 

Now using the Coulombs law to find for the electric force:

F = k q1 q2 / r^2 = k (Q)^2 / r^2

where k is a contant = 9 * 10^9 N m^2 / C^2

r = the distance of the two metals = 0.2 m

So,

F = (9 * 10^9 N m^2 / C^2) (1.564 * 10^-12 C)^2 / (0.2 m)^2

F = 5.51 * 10^-13 N

 

Since the two metals repel therefore they are the one which exerts the force hence the magnitude must be negative:

F = - 5.51 * 10^-13 N