Question

A point charge q moves from point $P$ to point $S$ along the path $PQRS$ (figure) in a uniform electric field $E$ pointing parallel to the positive direction of the X-axis. 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:

• A. $qEa$
• B. $-qEa$
• C. $qEa\sqrt{2}$
• D. $qE\sqrt{\left[\right(2a{)}^2+b^2]}$

Answer 1

The correct option is B $-qEa$

Now, Work done by the electric field is independent of the path

$W_{PQRS}=W_{PS}$

$=q(E_{x}dx+E_{y}dy+E_{z}dz)$

$=q(E(-a)+0+0)$

$=9E\sqrt{{\left(2a\right)}^2+b^2}$

$W_{PQRS}=-qaE$ or $-qEa$.