Module 2 : Electrostatics
Lecture 8 : Electrostatic Potential
  We use the spherical polar coordinates to express the length element $\vec{dl}$
 
\begin{displaymath}\vec{dl} = dr\hat r + r d\theta\hat\theta + r\sin\theta\hat\phi\end{displaymath}
  As the force is central, only the radial component of $\vec{dl}$contributes to the integral.
 
\begin{eqnarray*} W &=& \frac{Q}{4\pi\epsilon_0}\int_a^b \frac{1}{r^2}dr\\ &=& \frac{Q}{4\pi\epsilon_0} \left[\frac{1}{a}-\frac{1}{b}\right] \end{eqnarray*}
  which depends only on the end points. Line integral of the electric field around any closed path is zero.
   

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