Finding Electric Forces Between Identical Spheres

[batman1169200]

Homework Statement

Two identical conducting small spheres are placed with their centers 0.300m apart. One is given a charge of 12.0 nC and the other a charge of -18.0 nC. a) Find the electric force exerted by one sphere on the other. b) Next, the spheres are connected by a conducting wire. Find the electric force between the two after they have come to equilibrium.

Homework Equations

F_e = (k_e)*(q1*q2)/(r^2)

The Attempt at a Solution

k_e is a constant of 8.99e9 N*m^2/C^2
plug the rest but I just don't understand the signs that well. Also when do i use the directional equation.

 

[kkrizka]

For the signs, I suggest you think about what direction forces have depending on their charges instead of trying to to plug them into the equation.

 

[Moetasim]

I would like to first clarify that the equation you have provided is for the electric force between two point charges, not spheres. However, it can still be used to calculate the force between the two spheres if we consider each sphere as a point charge located at its center.

a) Using the given values, we can calculate the electric force between the spheres as:

F_e = (8.99e9 N*m^2/C^2) * (12.0e-9 C) * (-18.0e-9 C) / (0.300m)^2

= -3.6e-5 N

The negative sign indicates that the force is attractive, as the two charges have opposite signs.

b) When the spheres are connected by a conducting wire, they will reach equilibrium, meaning they will have the same potential and thus the same charge. The charge on each sphere will be equal to the average of the initial charges, which is (12.0e-9 C - 18.0e-9 C)/2 = -3.0e-9 C.

Now, using the same formula, we can calculate the electric force between the two spheres at equilibrium as:

F_e = (8.99e9 N*m^2/C^2) * (-3.0e-9 C) * (-3.0e-9 C) / (0.300m)^2

= 3.0e-5 N

Since the charges on both spheres are now negative, the force between them is repulsive.

The directional equation is used when the charges are not located at the center of the spheres, but rather at different points on the surface. In this case, the distance between the charges would be the distance between the two points on the surface, and the direction of the force would be along the line connecting the two charges. However, in this problem, since the charges are located at the center of the spheres, the distance between them is simply the distance between the centers of the spheres, and the direction of the force is along this line.