Work is done--and potential energy is altered--whenever two charges move toward or away from each other. Two like charges have more electric potential energy when they are near and less when they are far away. Two unlike charges have more electric potential energy when they are far apart and less when they are near each other. The change in electric potential energy PEAB is the opposite of the work done by external forces as two charges are moved,
PEAB = - WAB
If we think of charge Q as fixed and charge q as moveable, that is the change in electric potential energy as charge q moves from point A to point B.
The electric potential difference between A and B is this difference in electric potential energy of charge q as it moves from A to B divided by the charge q. Electric potential difference is written as V so that
This is also known as the voltage between A and B. Turning equation 18.2 around, we find that the electric potential energy of charge q changes by amount PEAB when it moves through a potential difference VAB,
PEAB = qVAB
If the voltage between points A and B is VAB and the voltage between B and C, VBC, then the voltage between A and C is VAC given by
VAC = VAB + VBC
That just means the work done in moving charge q from A to C is the same as moving the charge q from A to B and then from B to C.
Now define a reference point as being at zero potential. We will write the voltage at point A as VA, meaning the voltage relative to that reference point; that is, VA = VA(ref). Then
VAC = VA - VC
That is, the potential difference between two points is the difference in the voltage at the two points.
If a displacement r is parallel to the electric field E, then
V = - E r
E = -V / r
Electric field lines and equipotential lines or surfaces are always perpendicular.
A capacitor is an electric device or circuit element that stores charge and energy. The capacitance of the capacitor is given by
The electric potential energy stored in a capacitor is given by
PEcap = 1/2 QV = 1/2 CV2 = 1/2 Q2/C
Capacitors in series or parallel may be replaced by a single equivalent capacitor whose value can be calculated by
= + ... (series capacitors)
Ceq = C1 + C2 + C3 + ... (parallel capacitors)
(c) Doug Davis, 2002; all rights reserved
Return to Ch 18, Electric Potential and Capacitors