# Electric Field of Three Point Charges

## Homework Statement

Three point charges lie along a circle of radius r at angles of 30°, 150°, and 270° as shown in the figure below. Find a symbolic expression for the resultant electric field at the center of the circle.

## Homework Equations

$\vec{E}=\frac{k_{e}q}{r^{2}}$

## The Attempt at a Solution

The two positive charges' horizontal components will cancel out, and their vertical components will combine. This is for the two positive charges:

$=2\frac{k_{e}q}{r^{2}}sin(30)$

The negative charge is all in the vertical direction.

$=-2\frac{k_{e}q}{r^{2}}$

I pulled the -2 from -2q out front.

Combining them for the total field:

$=2\frac{k_{e}q}{r^{2}}sin(30)+-2\frac{k_{e}q}{r^{2}}$

$=2\frac{k_{e}q}{r^{2}}[sin(30)+1]$

How does that look?

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ehild
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Combining them for the total field:

$=2\frac{k_{e}q}{r^{2}}sin(30)+-2\frac{k_{e}q}{r^{2}}$

$=2\frac{k_{e}q}{r^{2}}[sin(30)+1)$

How does that look?
Well, "+-" identical "+" does not look nice :tongue2: Indicate the direction of the contribution of the separate charges to the electric field. So the two positive charges contribute with a downward electric field and that of the negative charge is also downward.

ehild

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