Electric Field of Three Point Charges

[crybllrd]

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?

 

[ehild]

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 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