Physics
posted by Alice .
Charge 2 × 10−18 C is on the y axis a distance 4 m from the origin and charge 9 × 10−18 C is on the x axis a distance d from the origin.
What is the value of d for which the
x component of the force on 9 × 10−18 C
is the greatest? The Coulomb constant is
8.98755 × 109 N · m2/C2.
Answer in units of m

The force of charges interaction is
F = k•q1•q2/r^2 = k•q1•q2/(d^2+4^2) = k•q1•q2/(d^2+16).
X projection is
Fx= k•q1•q2/(d^2+16) •cosα = k•q1•q2/(d^2+16) •d/(d^2+16)^1/2.
We have to find the derivative of Fx.
(Fx)´ = k•q1•q2[(d^2+16)^3/2 – 3d• (d^2+16)^5/2] = 0
Solving this equation, we find d = 2.83 m