Two fixed point charges +9e and +4e units are placed on a straight line AB= a at A and B respectively . Where should the third point charge be placed on AB for it to be in equilibrium ?

Explanation

For .q. to be in equilibrium,
` F_( qq_1) =F_(qq_2) `
ie. `(1)/( 4pi in _0) (q_1q)/( x^(2)) =(1)/( 4pi in _0) (q_2q)/( (a-x)^(2)) `
` (9e)/( x^(2)) =( 4e)/( (a-x) ^(2)) `
` 9( a-x)^(2) =4x^(2) " " 3(a-x) =+- 2x`
` (##JYT_AJP_AIO_PHY_XII_C01_SLV_012_S01##) `
Hence charges q should be placed at a distance of `(3a)/( 5) ` from the charge 9e on AB