(a) Show that at points along the axis of a dipole (along the same line that contains − Q {\displaystyle -Q} and + Q {\displaystyle +Q} ), the electric field has magnitude
E = 1 4 π ϵ 0 2 p r 3 {\displaystyle E={\frac {1}{4\pi \epsilon _{0}}}{\frac {2p}{r^{3}}}}
for r ≫ l {\displaystyle r\gg l} , where r {\displaystyle r} is the distance from a point to the center of the dipole.
(b) In what direction does E → {\displaystyle {\vec {E}}} point?
E net = E +Q + E -Q = Q 4 π ϵ 0 ( r − 1 2 l ) 2 + ( − Q ) 4 π ϵ 0 ( r − 1 2 l ) 2 {\displaystyle E_{\text{net}}=E_{\text{+Q}}+E_{\text{-Q}}={\frac {Q}{4\pi \epsilon _{0}\left(r-{\frac {1}{2}}l\right)^{2}}}+{\frac {(-Q)}{4\pi \epsilon _{0}\left(r-{\frac {1}{2}}l\right)^{2}}}}
and 
), the electric field has magnitude
, where 
is the distance from a point to the center of the dipole.
point?
