Set up arrangment of three point charges : `q, + 2q and x q` separated by equal finite distances so that electric potential energy of the system is zero. What is x ?

Answer

Charges `+q, + 2q and - (2q)/(3)` at vertices of an equillaterial traiangle ; `x = -2//3`

Explanation

Let the three charges be held at the vertices A.B.C of an equilateral triangle of each side = r, Fig

Potential energy of the system
`= (1)/(4pi in_(0)) [(q(2q))/(r ) + (2q (x q))/(r ) + (x q (+q))/(r )] = 0`
`(2q^(2))/(r) + (3q^(2) x)/(r) = 0`
`x = -2//3`