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 ${\vec {F}}$ 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:

${\vec {F}}=q_{t}\cdot {\vec {E}}$

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

The Electric Field of a Point Charge

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

${\vec {E}}=k_{e}{\frac {Q_{s}}{r^{2}}}{\hat {r}}$

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 ${\vec {F}}=q_{t}\cdot {\vec {E}}$, this simply gives you Coulomb's Law.

Other Videos

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