Six point charges each of the magnitude (Q ) are placed at the vertices of a regular hexagon of side (a ) as shown in the figure. Electric field intensity on the line passing through the centre (O ) and perpendicular to the plane of the figure at a large distance (x( > a) ) from (O ) is ( ( Let, 1 4 ₀ =k ) )

Step-by-step solution

According to the question, Let (O K=x ) due to (A B ), force at the point (K ) is only along (A B ) ( i.e., F_K= 2 k Q a (a^2+x^2 )^ 3 2 ) ( ) There are three such (F_K^ s ) so the net resultant of these three, ( aligned & F_ net = 4 k Q a (a^2+x^2 )^ 3 2 = 4 k Q a x^3 (1+ a^2 x^2 )^ 3 2 & F_ net = 4 k Q a x^3 ( a^2 x^2 =0 ),(x > > a) aligned )