Three equal charges + q are placed at the three vertices of an equilateral triangle centered at the origin. They are held in equilibrium by a restoring force of magnitude F(r)=k r directed towards the origin, where k is a constant. What is the distance of the three charges from the origin?

Step-by-step solution

F(r)=k T now F_ net on a particle is 2 F_ q 30^ due to the other two charges F _ net = 2 kq ² a ² 3 2 also r= 2 3 ( 3 2 a ) a = 3 r replacing it in F _ nat we get F _ net = 2 kq ² ( 3 r )² ( 3 2 )= kq ² 3 r ² this is balanced by F ( r ) array l F(r)=F_ n e t k r= 1 q² 4 ₀ 3 r² r= ( 3 q² 12 ₀ k )^ 1 / 3 array