Answers for E5 (rev. 3.0)
E-5. Electric Potential
Questions for discussion
1. True or false: A point charge placed in an external electric field accelerates toward the direction
of decreasing electric potential.
This is true for positive point charges. For a positive point charge, the situation is the same as that
of a ball on a hill. Just as the ball wants to move towards lower gravitational potential, the point
charge wants to move towards lower electric potential.
If the point charge is negative, then we just have to remember that the point charge wants to move
towards higher electric potential. Ultimately this is because the electric force on the point charge
is in the direction opposite to the electric field.
(If masses felt gravitational forces in the direction opposite the gravitational field, they'd move
towards higher potential too!)
2. A point mass m = 0.05 kg, with charge Q = +3 C, is sitting in an external potential Vi = 17 V.
How much work will it take to move the point charge to a point with higher potential Vf = 22 V?
When the point charge Q is sitting in an external potential Vi, the point charge has potential energy
Ui = Q Vi = 3C × 17 V = 51 J.
When the point charge Q is sitting at a point with higher potential Vf, then the point charge has a
correspondingly higher potential energy: Uf = Q Vf = 3 C × 22 V = 66 J.
Notice that the potential energy of the point charge has increased by 15 J. This must be the
amount of work we did to move it from the initial point to the final point.
More generally, we have the expression Wby you = Q (Vf - Vi).
This may all seem a bit abstract. Why, for example, did we have to do work? Remember the
analogy with gravitational potential: You have to do work to change the gravitational potential
energy of a baseball, and the reason is that gravitational potential energy is just another way of
accounting for gravitational forces.
Likewise, the electric field in our problem certainly ex