Question

(a) Calculate potential at a point at $9cm$ distance due to charge $4\times {10}^{-7}C$.
(b) Determine the work done in bringing a charge of $2\times {10}^{-9}C$ from infinity to that point. Does this work depend upon the path along which it was brought?

Answer 1

(a) Potential at point $P$
$\begin{array}{cc}V& =\frac{1}{4\pi {\epsilon }_0}\frac{Q}{r}\\ & =9\times {10}^9{Nm}^2{C}^{-2}\times \frac{4\times {10}^{-7}C}{0.09m}\\ & =4\times {10}^{4}V\end{array}$
(b) Work done in bringing charge $2\times {10}^{-9}C$ from infinity to point $P$
$W=qV$
$=2\cdot {10}^{-9}C\times 4\times {10}^{4}V$
$=8\times {10}^{5}J$
This work done does not depend on path follows.