Consider the electric dipole that we studied in our lecture on the last pages of Module $1.$ It had a charge $+q$ at $z=+\frac{d}{2}$ above the origin and a charge $-q$ at $z=-\frac{d}{2}$ below the origin. We then solved for the electric field at a height of $z$ up along the axis of the dipole, i$.$e$.,$ along the $z-$axis.

a$.$ Solve for the electric field at a distance $x$ to the right of the origin, i$.$e$.,$ along the $x-$axis. Draw the new system and be sure to solve for the magnitude and direction of the new electric field!

b$.$ What does this expression for the electric field become for very large $x$ values?