Module 2 : Electrostatics
Lecture 8 : Electrostatic Potential

Example 14 :

In a certain region of space, the potential function is given by the expression

\begin{displaymath}\phi(x,y,z) = x^2 + xy\end{displaymath}

where the potential is measured in volts and the distances in meters. Determine the electric field at the point $(2,1)$.
Solution :

Using

\begin{displaymath}\vec E = -\nabla\phi = -\hat\imath\frac{\partial\phi}{\partia... ...rac{\partial\phi}{\partial y} = (-2x-y)\hat\imath -x\hat\jmath\end{displaymath}

Substituting for $x$and $y$

\begin{displaymath}\vec E = -5\hat\imath -2\hat\jmath\end{displaymath}

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