Module 2 : Electrostatics
Lecture 8 : Electrostatic Potential

Example 11 :
Calculate the work done by the electric field due to a charge $Q$located at the origin to take a unit test charge from the point A to the point B, along the path shown.

Solution :

The force on the unit test charge due to the charge $Q$is, by definition, the electric field due to the charge $Q$,

$\displaystyle{ \vec E = \frac{1}{4\pi\epsilon_0}\frac{Q}{r^2}\hat r} $. The work done by the field on the test charge is

\begin{displaymath}W = \int_a^b \vec E\cdot \vec{dl}\end{displaymath}

where $\vec{dl}$is along the path connecting A and B.

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