Review of Basic Electrostatics

Part 2

Derivation of electric potential due to a single point charge Q

Applying (4) to the case of a single charge Q, notice

Therefore,

(5)


Relation between V and E

We obtained the expression for V [from (5)] from the expression for E [from (3)] using the definition in (4).

Conversely, given the potential V, the electric field is obtained by

(6)

where is the gradient operator.

For a collection of charges, the electric field can be calculated by applying Coulomb's Law, (1), to each individual charge and adding all the contributing fields. This involves vector addition.

A much simpler method is to obtain the total electric potential by adding the potentials due to individual charge and take its gradient by (6). This is because the potential is always a scalar (a plain number), and scalars are easier to deal with than vectors.

Move on to learn the Definition of Potential. You may also wish to examine some applications of what you have just learned.


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