SAT Physics Subject Test

Chapter 9 Electric Potential and Capacitance

When an object moves in a gravitational field, it usually experiences a change in kinetic energy and in gravitational potential energy because there is work done on the object by gravity. Similarly, when a charge moves in an electric field, it generally experiences a change in kinetic energy and in electrical potential energy because of the work done on it by the electric field. In this chapter we will discuss electric potentials.

ELECTRICAL POTENTIAL ENERGY

As we said, when a charge moves in an electric field, unless its displacement is always perpendicular to the field, the electric force does work on the charge. If WE is the work done by the electric force, then the change in the charge’s electrical potential energy is defined by


ΔUE = –WE


Notice that this is the same equation that defined the change in the gravitational potential energy of an object of mass m undergoing a displacement in a gravitational field (ΔUG = –WG).

  1. A positive charge +q moves from position A to position B in a uniform electric field E

What is its change in electrical potential energy?

Here’s How to Crack It

Since the field is uniform, the electric force that the charge feels, FE = qE, is constant. Since q is positive, FE points in the same direction as E, and, as the figure shows, they point in the same direction as the displacement, r. This makes the work (W = Fd) done by the electric field equal toWE = FEr = qEr, so the change in the electrical potential energy is

UE = –qEr

Notice that the change in potential energy is negative, which means that potential energy has decreased; this always happens when the field does positive work. It’s just like when you drop a rock to the ground: Gravity does positive work, and the rock loses gravitational potential energy.

  2. Solve the previous problem, but consider the case of a negative charge, –q.

Here’s How to Crack It

In this case, an outside agent must be pushing the charge to make it move because the electric force naturally pushes negative charges against field lines. Therefore, we expect that the work done by the electric field is negative. The electric force, FE = (–q)E, points in the direction opposite to the displacement, so the work it does is WE = –FEr = –qEr, and the change in electrical potential energy is positive: ∆UE = –WE = –(–qEr) = qEr. Since the change in potential energy is positive, the potential energy has increased; this always happens when the field does negative work. It’s like when you lift a rock off the ground: Gravity does negative work, and the rock gains gravitational potential energy.