Question

2. A point charge q sits at the origin and a point charge -4 is located at (, y, z) (d,d,-d), where d is some arbitrary unit of length. Determine the location (not infinitely far away) at which the electric field vanishes.

Answer 1

If E = 0 then E_x = 0, E_y = 0 and E_2 = 0 E_x = 0 implies kq/(-x)^2 + k (-4 q)/d^2 = 0 implies k q/x^2 - 4 k q/d^2 = 0 implies 1/x^2 = 4/d^2 implies x = d/2 but x is an negative x axis implies x = -d/2 simillarly y will be -d/2 implies y = -d/2 on z axis -4q change in an negative x axis therefore field will be zero at z = d/2 (positive z axis) implies z = d/2 therefore field will be zero at (-d/2, -d/2, d/2)