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Electric Field of Three Point Charges

  1. Jan 22, 2012 #1
    1. The problem statement, all variables and given/known data

    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

    2. Relevant equations

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

    3. 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?
     
  2. jcsd
  3. Jan 22, 2012 #2

    ehild

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    Homework Helper
    Gold Member

    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: Jan 22, 2012
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