![]() Gravitational potential energy and electric potential energy are quite analogous. PE can be found at any point by taking one point as a reference and calculating the work needed to move a charge to the other point. There must be a minus sign in front of ΔPE ΔPE to make W W positive. For example, work W W done to accelerate a positive charge from rest is positive and results from a loss in PE, or a negative ΔPE. There must be a minus sign in front of Δ PE Δ PE to make W W positive. For example, work W W done to accelerate a positive charge from rest is positive and results from a loss in PE, or a negative Δ PE Δ PE. The change in potential energy, Δ PE Δ PE, is crucial, since the work done by a conservative force is the negative of the change in potential energy that is, W = –Δ PE W = –Δ PE. We use the letters PE to denote electric potential energy, which has units of joules (J). When a force is conservative, it is possible to define a potential energy associated with the force, and it is usually easier to deal with the potential energy (because it depends only on position) than to calculate the work directly. This is exactly analogous to the gravitational force in the absence of dissipative forces such as friction. The electrostatic or Coulomb force is conservative, which means that the work done on q q is independent of the path taken. Work is done by a force, but since this force is conservative, we can write W = –Δ PE W = –Δ PE. In both cases potential energy is converted to another form. ![]() Figure 19.2 A charge accelerated by an electric field is analogous to a mass going down a hill. ![]()
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