Answer to Question #84745 in Electric Circuits for Nikita Koladiya

Question

Three charges q, 2q and q are to be placed on a straight wire of length 10 m. Determine the positions where the charges should to be placed so that the electrostatic potential energy of the system is a minimum.

Answer 1

U=k(〖2q〗^2/r+〖2q〗^2/((10-r))+q^2/10)=kq^2 (2/r+2/((10-r))+1/10)

We can minimize this by taking the derivitive with respect to r and setting it equal to 0:

0=kq^2 (-2/r^2 +2/(10-r)^2 +0)

-r^2/2=(10-r)^2/2

This has 2 solutions. However, we are only interested in solutions that lie along the 9cm line (solutions where r is positive), so r=10(√6-2)