Module 2 : Electrostatics
Lecture 9 : Electrostatic Potential
  Electric Field of a Dipole
A.
 CARTESIAN COORDINATES
It is convenient to define the cartesian axes in the following way. Let the dipole moment vector be taken along the z-axis and position vector $\vec r$of P in the y-z plane (We have denoted the point where the electric field is calculated by the letter P and the electric dipole moment vector as $\vec p$). We then have $\cos\theta = z/r$with $ r= \sqrt{y^2+z^2}$. Thus
 
\begin{displaymath}\phi(x,y,z) = \frac{p\cos\theta}{4\pi\epsilon_0r^2} = \frac{pz}{(y^2+z^2)^{3/2}}\end{displaymath}
  Since $\phi$is independent of $x$, $E_x=0$. The y and z components are
 
\begin{eqnarray*} E_y &=& -\frac{\partial}{\partial y}\left[\frac{pz}{4\pi\epsil... ...ilon_0(y^2+z^2)^{5/2}} = \frac{3p}{4\pi\epsilon_0}\frac{yz}{r^5} \end{eqnarray*}
   
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