Potential of a Point Charge
Please use the following derivation as a replacement for that in HRW Sec.5 of Ch.25.
The simplest example of the use of the definition of the electric potential,
is evaluation of the potential of a single point charge.
The electric field points radially away from the point charge:
The path is also chosen to be radially outward
so that the integrand of the line integral simplifies significantly:
With the appropriate choice of path, the line integral becomes a simple integral over r:
Using the convention of setting the potential to zero for infinite distance from the charge,
i.e.V = 0 for rB approaching infinity,
yields the following formula for the value
of electric potential at an arbitrary point from a point charge:
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Last updated Feb. 16, 1998.
Copyright George Watson, Univ. of Delaware, 1997.