Electric Potential Problem?

[AnnieF]

Homework Statement

Three charges are at the corners of an equilateral triangle (side L). Determine the potential at the midpoint of each of the sides.

Here is the picture:

http://www.solutioninn.com/physics/...es-are-at-the-corners-of-equilateral-triangle

Homework Equations

V= kQ/r

The Attempt at a Solution

Side 1 (Left Side):

-kQ/.5L-3q/.5L+kQ/sqrt(3/4)L= -4KQ/.5L+KQ/sqrt(3/4)L= -8KQ/L+ KQ/sqrt(3/4)L

Side 2 (Right Side):

-3kQ/.5L + kQ/.5L - kQ/sqrt(3/4)L = -4kQ/L- KQ/sqrt(3/4) L

Side 3 (top):

-kQ/.5 L + kQ/.5L- 3kQ/sqrt(3/4)L= -3KQ/sqrt(3/4)L

That is all I have.. I really don't feel like I am doing this right, and if I am I am not sure how to simplify these more..Is the problem looking for actual numbers?

 

[anathema]

Or is it okay to leave it as a variable?

Hello,

Thank you for your post. Your equations are correct, but you can simplify them further by factoring out common terms. Also, since the charges are all the same magnitude, you can use just one variable (Q) instead of kQ. The problem is looking for actual numbers, so you will need to plug in values for Q, L, and k in order to get a numerical answer for the potential at each midpoint.

Here is a simplified version of your equations:

Side 1 (Left Side):

V = -8Q/L + Q/sqrt(3/4)L = (-8 + 1/sqrt(3/4))Q/L = (-8 + 4/sqrt(3))Q/L

Side 2 (Right Side):

V = -4Q/L - Q/sqrt(3/4)L = (-4 - 1/sqrt(3/4))Q/L = (-4 - 4/sqrt(3))Q/L

Side 3 (Top):

V = -3Q/sqrt(3/4)L = (-3 + 4/sqrt(3))Q/L

I hope this helps! Let me know if you have any further questions.