(a) Three point charges q,-4q and 2q are placed at the vertices of an equilateral triangle ABC of side 'l' as shown in the figure. Obtain the expression for the magnitude of the resultant electric force acting on the charge q.
(b) Find out the amount of the work done to separate the charges at infinite distance.

Explanation

Force on charge q due to the charge -4q
` F_1 =(1)/( 4pi in _0alpha ) ((4q^(2))/( l^(2)) ` along AB
Force on the charge q. due to the charge 2q
` F_2 =(1)/( 4pin in _0) ((4q^(2))/( l^(2)) `along CA
the forces `F_1 and F_2 ` are inclined to each other at an angle of `120^(@) `
Hence , resultant electric force on charge q
` F= sqrt( F_1^(2) +F_2^(2) +2F_1F_2cos theta ) `
` =sqrt( F_1^(2) +F_2^(2) + 2F_1F_2cos theta 120^(@) ) `
` = sqrt( F_1^(2) +F_2^(2) -F_1F_2 ) `
` =((1)/( 4pi in _0) (q^(2) )/( l^(2))) sqrt( 16+4-8) `
` =(1)/( 4pi in _0) ((2sqrt3q^(2))/( l^(2)))`