Bringing 3 Charges from infinity into a triangle

[lilpoopoo]

Homework Statement

How much work is needed to arrange three charges, Q, into an equilateral triangle? The particles are initially infinitely far apart. Take 'a' to be the length of each side of the triangle.

Homework Equations

U = {(kqq)/L}

The Attempt at a Solution

I was under the assumption it takes no work to bring the first charge, Q1, from infinity since no other force is present.

To bring in charge #2 requires:

U = (kQ1Q2)/a = (kQ^2)/a

To bring in charge #3 requires a greater U since two charges are already present. I added the two pair-wise interactions of Q1 with Q3, and Q2 with Q3:

U = (kQ1Q3)/a + (kQ2Q3)/a = (2kQ^2)/a

Add both U's and get:

(3kQ^2)/a

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Is this correct?

 

[ehild]

Yes, it is correct.

ehild