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Electric Field of Three Point Charges

  • Thread starter crybllrd
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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.

23-p-026.gif


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?
 

Answers and Replies

  • #2
ehild
Homework Helper
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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?
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
 
Last edited:

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