Question

A point charge $ +q $ moves from point $ P $ to origin $ O $ along the path $ PQRO $ in a uniform electric field $ E $ . Find the work done by the field

• A. $ - 2qEa $
• B. $ 2qEa $
• C. $ 8qEa $
• D. $ - 4qEa $

Answer 1

Answer: (A)

As the electrostatic force are conservative, work done is independent of path. Effective displacement
in going from $P$ to $D$ along any path $= PO$
$= (0 - 2a) \hat{i} + (0 - b) \hat{j} + (0 - 0)\hat {k} = - 2a\hat{i} - b\hat{j}$
Force on charge, $F = (qE) \hat{i}$
Now, work done $= F \cdot PO = (qE\hat{i}) \cdot (- 2a\hat{i} - b\hat{j})$
$= - 2qE\, a$