a particle with charge Q is on the y axis a distance a from the origin and a particle with charge qi is on the x axis at a distance d from the origin. The value of d for which the x component of the force on the second particle is the greatest is

Force on Q due to q₁

= k Q. q₁ / r², r is distance between two.

X component

= k Q. q₁ / r² x cos θ, θ is angle r makes with x - axis.

= k Q. q₁ / r² x cos θ

r = a / sinθ

X component

= k Q. q₁ sin²θ. cosθ / a²

= k Q. q₁ / 2 a² x sin2θ. sinθ

for maximum value of it,

sin2θ = 1, θ = 45°

a / d = tan45

a = d.