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.

Electric Field Lines

Electric field lines visually represent the direction and strength of an electric field around charges. They point in the direction the electric force would have on a positive test charge.

• **Direction**: Field lines point away from positive charges and toward negative charges.
• **Density**: The closer the lines, the stronger the electric field in that area.

Rules for Drawing Electric Field Lines

• Lines start or end on charges, with more lines indicating a larger charge magnitude.
• Field lines never cross.
• They form continuous, smooth curves.

Other Videos

MIT Physics Demo -- Faraday's Cage

Simulations

• PhET Simulation: Electric Field of Dreams
  
• PhET Simulation: Charges and Fields
  
• PhET Simulation: Electric Field Hockey
  
• PhET Simulation: Radio Waves & Electromagnetic Fields
  
• PhET Simulation: Microwaves
  

Other Links

Electric Field vectors

The Electric Field

The Electric Field-3D

Lightning applet

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