- #1

- 120

- 0

## 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

[itex]\vec{E}=\frac{k_{e}q}{r^{2}}[/itex]

## 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:

[itex]=2\frac{k_{e}q}{r^{2}}sin(30)[/itex]

The negative charge is all in the vertical direction.

[itex]=-2\frac{k_{e}q}{r^{2}}[/itex]

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

Combining them for the total field:

[itex]=2\frac{k_{e}q}{r^{2}}sin(30)+-2\frac{k_{e}q}{r^{2}}[/itex]

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

How does that look?