#### Potential Energy in a Non-Uniform Field

The potential energy for two point charges separated by a distance r is:

U =
 kqQ r

A positive charge with mass m and charge +q is placed near a placed near a fixed positive charge +Q, where Q is much larger than q. The field shown is from the charge Q. Which charges feels a larger force? Consider only the forces the charges exert on one another.

1. The +q charge feels a larger force
2. The +Q charge feels a larger force
3. The forces are equal

In case 2 a negative charge of mass m and charge -q is placed at the point where the +q charge was. It feels a force of the same magnitude as the +q charge did, but in the opposite direction.

Define the potential energy to be zero when the charges are infinitely far apart. In which case is the potential energy greatest?

1. Case 1, with +q and +Q
2. Case 2, with -q and +Q
3. The potential energy is equal in both cases

Case 1, because the potential energy is positive. The potential energy is negative in case 2.

As with the uniform field situation the charges move in the direction of decreasing potential energy when they are released from rest.

Imagine releasing the charges from rest and observing them for a particular time interval. Assuming no collisions have taken place, at the end of that time interval which charge will have the greatest speed?

1. The +q charge
2. The -q charge
3. Both charges will have the same speed

The -q charge will be moving fastest.

The negative charge will move toward the +Q charge. The closer it gets the larger the force gets and the larger the acceleration. Just the opposite is true for the +q charge.