The Electric Field

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Textbook

University Physics Volume 2: Chapter 5.4

Theory

Electric Field

The electric field acts as a shortcut for calculating the electric force $\overrightarrow{F}$ on a test charge $q$, similar to how the gravitational field $g$ simplifies calculations for gravitational force. Instead of recalculating the force based on Coulomb's Law (and adding the forces of multiple source charges), we can use the electric field, where:

$\overrightarrow{F}=q_t\cdot \overrightarrow{E}$

In the same way that $\overrightarrow{g}$ gives the gravitational force per kilogram, $\overrightarrow{E}$ gives the electric force per coulomb.

The Electric Field of a Point Charge

The electric field $\overrightarrow{E}$ caused by a point (source) charge $Q_s$ at a distance $r$ from the position is given by:

$\overrightarrow{E}=k_e\frac{Q_s}{r^2}\hat{r}$

where:

• $k_e$ is the electrostatic constant, approximately $8.99\times 10^9{\text{N m}}^2/{\text{C}}^2$.
• $Q_s$ is the point charge creating the electric field (the source charge).
• $r$ is the distance from the charge to the point where the field is being calculated.
• $\hat{r}$ is a unit vector pointing from the charge to the point of interest.

Note that combined with $\overrightarrow{F}=q_t\cdot \overrightarrow{E}$, this simply gives you Coulomb's Law.

Other Videos

MIT Physics Demo -- Faraday's Cage

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