A particle with charge Q is on the y-axis a distance A from the origin and another particle with charge q is on the x-axis 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:A) 0B) AC) √2AD) A/2

E) A√2

Fxi (max) for A = 0

Explanation:

The electric force between two charges is given by Coulomb's law

F = (1/4*π*ε₀) * q₁*q₂ / d²

For simplicity (1/4*π*ε₀) = K

F = K * q₁*q₂ / d²

Of course a force is a vector, in our case we have certain distribution of charges. Charge Q on the y axis, and q on the x axis. These two charges are positive, then they will reject each other, and the direction of the force will be the same direction of (L) the hypotenuse in right triangle AOD.

In all cases as the force is a vector the maximum value of any of its components is when that component is equal to the force, that is

as Ft = Fxi + Fyj

Fxi maximum when Fxi = Ft and Fyi = 0 or

Fyj maximum when Fyj = Ft and Fxi = 0

Remember that Fxi = Ft * cos θ (θ the angle between x axis and the direction of the force) therefore for Fxi to be maximum cosθ must be equal to 1, θ = 0, then the direction of Fx is the same as that for Ft. That is the required condition, then

Fxi (max) for A = 0