help please! L. Three point charges have charges 2 triangle with side lengths 3d

Question

help please!

L. Three point charges have charges 2 triangle with side lengths 3d. 4d, and 5d. Each of the three possible arrangements are shown below labeled A-C. Note, the values of Q and d are such that kQ/d 10J Q. 2Q, and 4Q. They will be placed at the corners of a right 24 20 4d 5d 4d Sd d 5d d--3d-b 24 ó--3-b 1Q 20 20 24 (a) Which arrangement resquires the least amount of energy to put together? Compute its arrangement energy (b) Which arrangement requires the greatest amount of energy to put together? Compute its arrangs- ment energy

Explanation / Answer

Here we need to find the potential energy of the system means we need to find work done

Note that work done is equal to change in electric potential energy.

For first triangle,

U = k*2Q*4Q/4d + k*2Q*2Q/3d + k*4Q*2Q/5d

U = kQ/d (8Q/4 + 4Q/3 + 8Q/5)

U = 4.933Q joules

For second triangle

U = 5.466Q joules

For third triangle

U = 5.266Q joules

As we can see, triangle (a) requires least amount of energy and and triangle (b) requires max energy.  

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