Module 2 : Electrostatics
Lecture 9 : Electrostatic Potential
  GENERAL EXPRESSION
  A respresentation independent form for the dipole field can be obtained from the above
  We have
\begin{eqnarray*} \vec E &=& E_r\hat r + E_\theta\hat\theta\\ &=& \frac{p}{4\pi... ...lon_0r^3}\left[ 2\cos\theta\hat r + \sin\theta\hat\theta \right] \end{eqnarray*}
  Using $\vec p = p\cos\theta\hat r - p\sin\theta\hat\theta$, we get
 
\begin{displaymath}\vec E = \frac{1}{4\pi\epsilon_0r^3}\left[(3\vec p\cdot\hat r)\hat r - \vec p\right]\end{displaymath}
  This form does not depend on any particular coordinate system. Note that, at large distances, the dipole field decreases with distance as $1/r^3$where as monopole field (i.e. field due to a point charge) decreases as $1/r^2$.
   
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