Point Charge

This page is all about the Electric Field due to a Point Charge.

Electric Field

A Work In Progress by Brandon Weiner: bweiner6 (talk)

A Mathematical Model of Electric Field due to Point Charge

The Electric Field of a Point Charge can be found by the formula:

[math]\displaystyle{ \vec E=\frac{1}{4 \pi \epsilon_0 } \frac{q}{r^2} \hat r,\text{where } \frac{1}{4 \pi \epsilon_0 } \text{is approximately } 9*10^{9} \text{, q is the charge of the particle,} \text{r is the magnitude of the distance} \text{ between the point charge and the observation point, and } }[/math] [math]\displaystyle{ \hat r \text { is the direction of the distance from } \text{the point charge to the observation point.} \text{This equation becomes when multiplied by a second particles's charge. } }[/math]

A Computational Model

Here is a link to some code which shows the Electric Field due to an Proton at different points.

Examples

Problem 1: There is a proton at <1,2,3>. Calculate the electric field at <2,-1,3>.

Step 1: Find [math]\displaystyle{ \hat r }[/math]

Find [math]\displaystyle{ \vec r_{obs} - \vec r_{proton} (\lt 2,-1,3\gt - \lt 1,2,3\gt = \lt 1,-3,0\gt ) }[/math]

Calculate the magnitude of r. ([math]\displaystyle{ \sqrt{1^2+(-3)^2+0^2}=\sqrt{10} }[/math]

From r, find the unit vector [math]\displaystyle{ \hat{r}. }[/math] [math]\displaystyle{ \lt \frac{1}{\sqrt{10}},\frac{-3}{\sqrt{10}},\frac{0}{\sqrt{10}}\gt }[/math]

Step 2: Find the magnitude of the Electric Field

[math]\displaystyle{ E= \frac{1}{4 \pi \epsilon_0 } \frac{q}{r^2} = \frac{1}{4 \pi \epsilon_0 } \frac{1.6 * 10^{-19}}{10} }[/math]

Step 3: Multiply the magnitude by [math]\displaystyle{ \hat{r} }[/math] to find the Electric Field

E= [math]\displaystyle{ \frac{1}{4 \pi \epsilon_0 } \frac{1.6 * 10^{-19}}{10}*\lt \frac{1}{\sqrt{10}},\frac{-3}{\sqrt{10}},\frac{0}{\sqrt{10}}\gt =\lt 4.554*10^{-11},-1.366*10^{-10},0\gt N/C }[/math]

Connectedness

1.How is this topic connected to something that you are interested in?

I am very interested in the idea of forces and how objects interact with each other. After you calculate the Electric Filed you can easily find the Electric Force on particle exerts on another.

2.How is it connected to your major?

I am a CompE major and so Electric Fields have to do with my major because when you integrate them with respect to dL, and swap the sign, you get potential difference(voltage), which is very important in circuits. As ECE majors take circuits classes, this topic is relevant to me.

3.Is there an interesting industrial application?

An interesting application is that electric fields of point charges can be used to find forces. Then you can predict the motion of various particles by the forces acting on them.

History

In the 1780s a French scientist named Charles Coulomb published many scientific papers on electricity and magnetism. While doing experiments, Coulomb had discovered an inverse square relationship between the amount of electric field and the distance between two particles and the electric field pointed in a line between the particles.

Also, he discovered that the charge of an particle (ie. positive or negative) determined the direction of the electric field (either a repulsion or attraction).

From these observations, as well as the use of fundamental constants, Coulomb's Law was created.

Charles-Augustin de Coulomb. (n.d.). Retrieved December 3, 2015, from https://nationalmaglab.org/education/magnet-academy/history-of-electricity-magnetism/pioneers/charles-augustin-de-coulomb

Shech, E., & Hatleback, E. (n.d.). The Material Intricacies of Coulomb’s 1785 Electric Torsion Balance Experiment. Retrieved December 3, 2015, from http://philsci-archive.pitt.edu/11048/1/The_Material_Intricacies_of_Coulomb's_1785_Electric_Torsion_Balance_Experiment_(EV).pdf

Point Charge

Contents

Electric Field

A Mathematical Model of Electric Field due to Point Charge

A Computational Model

Examples

Connectedness

History

See also

Further reading

External links

References

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