Electric Field

Source lecture(s): SC134 Lec2-3

Intuition

A charge creates a field around it; other charges feel forces through that field without touching.

Formal Definition

$$\vec{E} = \frac{\vec{F}}{q_0}$$ for a test charge $q_0\to0$.

Mathematical Formulation

Point charge: $$\vec{E} = \frac{1}{4\pi\varepsilon_0}\frac{q}{r^2}\hat{r}$$ Continuous distribution: $$\vec{E} = \int \frac{1}{4\pi\varepsilon_0}\frac{dq}{r^2}\hat{r}$$

Derivation

Measure force per unit test charge; superposition allows summation/integration over distributions.

Worked Example

Two equal charges at $x=\pm a$: on the $y$-axis, $E_x$ cancels, leaving $E_y = (1/4\pi\varepsilon_0)2qy/(a^2+y^2)^{3/2}$.

Common Mistakes

Using $E = kq/r$ instead of $kq/r^2$.
Forgetting vector direction from source to field point.

Quiz

Q1. What is the unit of electric field?

Answer

N/C or V/m.