Posted by B.Y.SARAT on Saturday, March 31, 2012 at 9:03am.
2 PARTICLES [FREE TO MOVE] WITH CHARGES +q and +4q are a distance L APART. A 3RD CHARGE IS PLACED SO THAT THE ENTIRE SYSTEM IS IN EQ2UILIBRIUM.FIND THE LOCATION,MAGNITUDE AND SIGN OF THE 3RD CHARGE

PHYSICS  drwls, Saturday, March 31, 2012 at 9:31am
The third charge must be placed between the q and 4q charges, so that there are equal and opposite forces along the line between the charges. The distance from the q charge must be half the distance from the 4q charge, so that Q/d^2 is the same for both.
Therefore, the third charge must be 1/3 of the way from q to 4q. That will be L/3 from charge q.