Module 2 : Electrostatics
Lecture 10 : Potential Energy of a System of Charges

Example 18 :
Determine the equipotential surface of an infinite line charge carrying a positive charge density $\lambda$.

Solution :
Let the line charge be along the z- axis. The potential due to a line charge at a point P is given by

\begin{displaymath}\phi(r) = -\frac{\lambda}{2\pi\epsilon_0}\ln r\end{displaymath}

where $r$is the distance of the point P from the line charge. Since the line charge along the z-axis, $ r= \sqrt{x^2+y^2}$so that

\begin{displaymath}\phi(r) = -\frac{\lambda}{4\pi\epsilon_0}\ln(x^2+y^2)\end{displaymath}


The surface is given by

\begin{displaymath}\ln(x^2+y^2) = -\frac{4\pi\epsilon_0\phi_o}{\lambda}\end{displaymath}

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