## Monday, November 26, 2012

### Potential Energy In An External Field

Potential energy of a single charge

The external electric field E and the corresponding external potential V may vary from point to point. By definition, V at a point P is the work done in bringing a unit positive charge from infinity to the point P.

Work done in bringing a charge q from infinity to the point P in the external field is qV. This work is stored in the form of potential energy of q. If the point P has position vector r relative to some origin, we can write:

Potential energy of a system of two charges in an external field

Work done in bringing the charge q1 from infinity to r1 is q1 V(r1). Consider the work done in bringing q2 to r2. In this step, work is done not only against the external field E but also against the field due to q1.
Work done on q2 against the external field

Work done on q2 against the field due to q1

By superposition principle for fields, add up the work done on q2 against the two fields. Work done in bringing q2 to r2

Thus, Potential energy of the system = the total work done in assembling the configuration