

Electric Potential, V at a Point in an
Electric Field 

The potential at a point in a field is the work done per
unit charge moving a small positive charge from infinity
to that point. 

Therefore, the units of V are JC^{1} 

As with gravitational potentials, the zero of electrical
potential is at infinity* but electrical potentials can be positive
or negative depending on whether work is done against the field or
by the field. 

*Remember that this just means, far enough away for the field
strength to have fallen to an undetectable value... 



If the potential at point A is V_{A}
and the potential at point B is V_{B} then the potential
difference, V, between the A and B is given, not surprisingly,
by 



We tend to use V for
potential differences and V plus subscript for potential at a point. 

If a charge, q, is moved through a potential difference, V, we
can write 



As in the case of electric field strength,
we usually miss out the "+" sign. It is included here as a reminder
that the definitions of potential and potential difference are based
on moving a positive charge. 



Potential at a Distance r from a Point Charge Q 



To find a figure for the potential at point
p we have to imagine bringing a small positive test charge from
infinity (a very long way away!) to
p. 

This task is complicated by the fact that the force varies in
strength as the charge is moved. 

This can be done by considering moving the test charge through
very small steps (steps small enough to allow us to consider the
force to be essentially constant) and then adding up the effects of
all these small steps by the mathematical process of integration. 

Doing this we find 


