12.4.1 Electric Potential

An electric charge moving in an electric field can lose or gain KE thanks to the work done by the electric force. Doesn’t this remind you of a mass gaining or losing KE as it rolls up or down a hill? Likewise, we can imagine an electric field as an electric landscape with electric hills and valleys etc. The “electric height” at each point is called electric potential.

While the gravitational potential is GPE per unit mass, the electric potential V is EPE per unit POSITIVE charge[1]. Conceptually (but not practically) speaking, we can determine the electric potential at a particular position with the help of a tiny test charge q. For example, if a +3.0 nC charge has EPE of −6.0 nJ when placed at a particular position, the electric potential at that position would be

\displaystyle \begin{aligned}V&=\frac{{EPE}}{q}\\&=\frac{{-6.0\times {{{10}}^{{-9}}}}}{{3.0\times {{{10}}^{{-9}}}}}\\&=-2.0\text{ J }{{\text{C}}^{{-1}}}\end{aligned}

Conversely, an electric charge q placed in an electric field where the electric potential is V will have an EPE of

\displaystyle EPE=qV

Note that by definition, the sign of the electric potential (at a point) follows the sign of the EPE for a positive test charge (placed at that point). So at a position where V is positive, a positive test charge would have positive EPE, but a negative test charge would have negative EPE.

Video Explanation

Electric “Elevation”

Concept Test

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[1] Remember that EPE is positive for a pair of like charges, but negative for a pair of unlike charges. This means that the EPE of a positive charge is opposite in polarity to that of a negative charge (placed at the same position in the electric field). As such, we have to specify the polarity of the test charge in order to define the polarity of the electric potential. As usual, the positive charge is chosen over the negative charge.

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