A positively charged sphere with a charge of the of 8Q is separated from a negatively charged sphere - 2Q by a distance r. The spheres briefly touch each other and move to the original distance are. what is the new force on each sphere inn terms of F

The new force is:

F1 = -(9/16)*F0

where F0 is the initial force.

Explanation:

The charges of the spheres is q1 = 8Q and q2 = -2Q

and as you know, the force between charged objects is:

F = k*q1*q2/r^2

where k is a constant and r is the distance

F0 = -(k16Q^2)/r^2

where the negative sign means that the force is attractive.

Now, when the spheres touch each other, the charge must be distributed equally in both spheres. So the total charge is q1 + q2 = 8Q - 2Q = 6Q

then each sphere has now a charge of 3Q.

The new force is:

F1 = k*3Q*3Q/r^2 = (k*9*Q^2)/r^2 = -(9/16)*F0

You can see that F1 is positive, this means that the force now is repulsive.