Introductory Physics Volume Two

38 Electric Potential 2.1
It is important to notice that the definition of electric potential
only tells us how to find the difference (V B − V A ) between the electric
potential at two different points, A and B . The value of the electric
potential itself is not defined. This is not a problem because only the
difference has physical significance. You may recall that this is true
for potential energy also. The potential energy at ten meters above
the surface of the earth is not defined, but the difference between the
potential energy at ten meters and three meters is defined, ∆U =
mg∆y. One can choose some point in space that is defined to be
the zero of the electric potential. This point is sometimes called the
ground. Then in reference to ground, all points have an absolute electric
potential. This is like choosing the surface of the earth as the zero of
gravitational potential energy.
Often the electric potential is simply referred to as the potential.
The units of electric potential is evidently the units of energy divided
by the units of charge. This unit occurs frequently and has it’s own
name, the Volt.
1Volt =
1Joule
1Coulomb
This unit is abbreviated as V. Be warned that this is a bad coincidence
since the symbol used for the electric potential is V , which is very
similar to V. This is not a serious problem, but if you mix up the
symbols, you can end up doing silly things with the algebra.
Example
Suppose that there is a uniform electric field ⃗ E = (0.2 N C
)î. The electric
potential difference between the two points ⃗r A = (1.0m)î+(2.0m)ĵ and
⃗r B = (5.0m)î + (−3.0m)ĵ is computed as follows.
V B − V A = ∆V = − ⃗ E · ∆⃗r
= −(0.2 N C
)î · [⃗r B − ⃗r A ]
= −(0.2 N C
)î · [(4.0m)î + (−5.0m)ĵ]
= −(0.2 N C
)(4.0m) + 0 = −0.8V
This example demonstrates that the electric potential decreases as
one moves in the direction of the electric field (positive x in this case).
This is a general rule: the electric field points from regions of high
electric potential to regions of low electric potential.