Question

Fill in the blank.
A point charge $q$ moves from point $P$ to point $S$ along the path $PQRS$ in a uniform electric field $E$ pointing $P$ parallel to the positive direction of the $x-$axis. The coordinate of the point $P,Q,R$ 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_________.

Answer 1

Work done by the electric field is path independent.

$W_{PQRS}=W_{PS}$

$\Rightarrow W_{PQRS}=q[E_x{d}_x+E_y{d}_y+E_z{d}_z]$

$\Rightarrow W_{PQRS}=q\left[E\right(-a)+0+0]$

$\Rightarrow W_{PQRS}=qaE$