Q.
A point charge $q$ moves from point $\overset{P}{\rightarrow}$ to point S along the path PQRS in a uniform electric field $\overrightarrow{E}$ pointing parallel to the positive direction of the $x$-axis, figure. The coordinates of the points P, Q, R and S are (a, b, 0), (2a, 0, 0), (a, -b, 0) and (0, 0, 0) respectively. The work done by the field in the above process is given by the expression
A) $qE$
B) $- qaE$
C) $q(\sqrt{a^{2} + b^{2})}E$
D) $3qE\sqrt{a^{2} + b^{2}}$
Explanation
(b) As the electrostatic force are conservative, work done is independent of path .
$W = \overrightarrow{F}.\ \ \overrightarrow{ds} = q\ E\widehat{\dot{i}}.\left\lbrack (0 - a)\widehat{\dot{i}} + (0 - b)\widehat{\dot{j}} \right\rbrack$
$= - q\ E\ a$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.