Tuesday, July 15, 2008
Electric potential
Consider a circle and the point P in the middle. If a positive charge is found somewhere on the circle a distance r from P , you can calculate the electric potential at P , V = kQ/r. This potential is positive. If a positive charge q is brought from infinity where the potential is zero, the external work done = qV (work done against electric field).A negative charge -q from infinity to point P would have involved the same energy but work done by the electric field. So it is wise to just calculate the magnitude of work done and decide to call it work done against /by electric field.
If a negative charge Q is somewhere on the circle , the potential at P is now zero, hence no work done in bringing charge q. Imagine q is attracted/repelled by -Q/+Q. This is scalar as the location of Q is not important only the sign + or - is taken into account.
Extend the problem to +10Q and -12Q found around on the circle , the potential at P would be V = k(-12Q+10Q)/r = -2kQ/r.
V and E are scalar and vector their positive and negative value do not mean the same thing. V negative means presence of negative charge. E negative means pointing to the left if you define right as positive or down if you define up as positive).
E negative has no reference to negative charge as V negative has not reference to direction. E and V are a world of difference.