[PHYS208 logo] Potential of a Point Charge

Please use the following derivation as a replacement for that in HRW Sec.5 of Ch.25.

Choice of path for evaluating potential of a point charge The simplest example of the use of the definition of the electric potential,

Formula to find V from E

is evaluation of the potential of a single point charge. The electric field points radially away from the point charge:

Electric field due to a point charge

The path is also chosen to be radially outward

Differential line element

so that the integrand of the line integral simplifies significantly:

Integrand of line integral

With the appropriate choice of path, the line integral becomes a simple integral over r:

Conversion from line integral to simple integral

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:

Potential of a point charge

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Last updated Feb. 16, 1998.
Copyright George Watson, Univ. of Delaware, 1997.