Is the electrical potential energy of two point charges positive or negative if the charges are of the same sign? Opposite signs? How does this relate to the work necessary to bring the charges into proximity from infinity? Hence, because the electric force is related to the electric field by F → = q E → F → = q E →, the electric field is itself conservative. Recall that this is how we determine whether a force is conservative or not.

One implication of this work calculation is that if we were to go around the path P 1 P 3 P 4 P 2 P 1, P 1 P 3 P 4 P 2 P 1, the net work would be zero ( Figure 7.6). Therefore, the only work done is along segment P 3 P 4, P 3 P 4, which is identical to P 1 P 2. Since the force on Q points either toward or away from q, no work is done by a force balancing the electric force, because it is perpendicular to the displacement along these arcs. The segments P 1 P 3 P 1 P 3 and P 4 P 2 P 4 P 2 are arcs of circles centered at q. Therefore, work on paths P 1 P 2 P 1 P 2 and P 1 P 3 P 4 P 2 P 1 P 3 P 4 P 2 are equal. The work on segments P 1 P 3 P 1 P 3 and P 4 P 2 P 4 P 2 are zero due to the electrical force being perpendicular to the displacement along these paths. We call this potential energy the electrical potential energy of Q.įigure 7.5 Two paths for displacement P 1 P 1 to P 2. The work done by the applied force F → F → on the charge Q changes the potential energy of Q. To show this explicitly, consider an electric charge + q + q fixed at the origin and move another charge + Q + Q toward q in such a manner that, at each instant, the applied force F → F → exactly balances the electric force F → e F → e on Q ( Figure 7.3). It is usually easier to work with the potential energy (because it depends only on position) than to calculate the work directly. When a force is conservative, it is possible to define a potential energy associated with the force. This is exactly analogous to the gravitational force.

The electrostatic or Coulomb force is conservative, which means that the work done on q is independent of the path taken, as we will demonstrate later. Work is done by a force, but since this force is conservative, we can write W = – Δ U W = – Δ U. In both cases, potential energy decreases as kinetic energy increases, – Δ U = Δ K – Δ U = Δ K. Figure 7.2 A charge accelerated by an electric field is analogous to a mass going down a hill.

Electric flux equation cube