Question

Point charge (q) moves from point (P) to point (S ) along the path PQRS as shown in fig. in a uniform electric field E, Pointing coparallel to the positive direction of the x-axis. The co-ordinates of the points P,Q,R,S are (a,b,0) , (2a,0,0) , (a,-b,0) , (0,0,0) respectively. The work done by the field in the above process is given by the expression

• A. q E q
• B. -q E a
• C. q E a$\sqrt{2}$
• D. q E $\sqrt{(2a{)}^2+b^2}$

Answer 1

The correct option is B -q E a

Work done $\overrightarrow{E}$ is independent of path.

$W_{PQRS}=W_{PS}=q[E_x{d}_x+E_y{d}_y+E_z{d}_z]=q\left[E\right(-a)+0+0]=-qEa$

Negative sign here shows that work has been done against field.