Electric Field

• Given several point charges the total force on another point charge is the summation of forces from the individual point charges

$$\mathbf{F}={\mathbf{F}}_1+{\mathbf{F}}_2+\cdots =\frac{1}{4\pi {ϵ}_0}\left(\frac{q_{1}Q}{r_1^2}\widehat{r_1}+\frac{q_{1}Q}{r_2^2}\widehat{r_2}+\dots \right)$$

• This sucks. Lets use the electric field instead.
• We define the electric field as:

$$\mathbf{E}(\mathbf{r})=\frac{1}{4\pi {ϵ}_0}\sum _{i=1}^n\frac{q_i}{r_i^2}{\hat{r}}_i$$

• And the force from the electric field on a point charge Q is given by

$$\mathbf{F}=Q\mathbf{E}$$

• The electric field is a function of position.
• It is a vector quantity.