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

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 9E9, q is the charge, r is the magnitude of the distance between the point charge and the observation point, and } }[/math] [math]\displaystyle{ \hat r \text { is the direction of the distance from the point charge to the observation point.} }[/math]

A Computational Model

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Examples

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Simple

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

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