# Electrical Potential Energy

#### umdnjmed

10+ Year Member
5+ Year Member
I have a couple of questions about electrical potential energy;

1) How does electrical potential energy vary with distance in an electric field caused by a positive point charge? Will it depend on whether the charge being introduced into the field is negative or positive?

2) This relates to the first question; electrical potential energy is supposedly analogous to gravitational potential energy and the latter increases with height. The two equations for electrical potential energy are U=qEd and U=kq1q2/r. Why is the relationship between U and d in the first one directly proportional while that between U and r in the second is inversely proportional?

#### hiaips

5+ Year Member
I have a couple of questions about electrical potential energy;

1) How does electrical potential energy vary with distance in an electric field caused by a positive point charge? Will it depend on whether the charge being introduced into the field is negative or positive?

2) This relates to the first question; electrical potential energy is supposedly analogous to gravitational potential energy and the latter increases with height. The two equations for electrical potential energy are U=qEd and U=kq1q2/r. Why is the relationship between U and d in the first one directly proportional while that between U and r in the second is inversely proportional?
1) Yes, the sign of the PE in that case depends on whether the second charge is positive or negative. However, the absolute values are the same (refer to the second equation that you post in your second question).

2) They aren't exactly analogous, because there are two kinds of charges (positive and negative). For example, if you have two like charges (positive or negative), you'll note that the electrical PE will actually decrease as these charges move further apart. This occurs because the forces are repulsive (whereas the gravitational force is always attractive). Potential energy generally decreases in the direction of the acting force, and nature generally wants to arrange objects or particles so that their potential energies are minimal.

As far as your equations are concerned: Both are actually inversely proportional to d. (Note that the first equation relates U to E, and in the case of a point charge, E varies as 1/d^2.)

Hope this helps...