The Electric Field: Difference between revisions
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In the same way that <math> \vec{g} </math> gives the gravitational force per kilogram, <math> \vec{E} </math> gives the electric force per coulomb. | In the same way that <math> \vec{g} </math> gives the gravitational force per kilogram, <math> \vec{E} </math> gives the electric force per coulomb. | ||
=== The Electric Field of a Point Charge === | |||
The electric field <math> \vec{E} </math> caused by a point (source) charge <math> Q_s </math> at a distance <math> r </math> from the position is given by: | |||
<math> \vec{E} = k_e \frac{Q_s}{r^2} \hat{r} </math> | |||
where: | |||
* <math> k_e </math> is the electrostatic constant, approximately <math> 8.99 \times 10^9 \, \text{N m}^2/\text{C}^2 </math>. | |||
* <math> Q_s </math> is the point charge creating the electric field (the source charge). | |||
* <math> r </math> is the distance from the charge to the point where the field is being calculated. | |||
* <math> \hat{r} </math> is a unit vector pointing from the charge to the point of interest. | |||
Note that combined with <math> \vec{F} = q_t \cdot \vec{E} </math>, this simply gives you Coulomb's Law. | |||
<youtube>qMnQQudvaE4</youtube> | <youtube>qMnQQudvaE4</youtube> | ||
Revision as of 11:31, 5 November 2024
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Textbook
University Physics Volume 2: Chapter 5.4
Electric Fields Videos
Theory
Electric Field
The electric field acts as a shortcut for calculating the electric force on a test charge , similar to how the gravitational field 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:
In the same way that gives the gravitational force per kilogram, gives the electric force per coulomb.
The Electric Field of a Point Charge
The electric field caused by a point (source) charge at a distance from the position is given by:
where:
- is the electrostatic constant, approximately .
- is the point charge creating the electric field (the source charge).
- is the distance from the charge to the point where the field is being calculated.
- is a unit vector pointing from the charge to the point of interest.
Note that combined with , this simply gives you Coulomb's Law.
Electric Field Lines
Typical Problems with the Electric Field
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
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