Q. A point charge q moves from point P to point S along the path PQRS in a uniform electric field $ \vec { 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 given by the expression
(a) qaE
(b) −qaE
(c) $\displaystyle q E \sqrt{a^2 + b^2} $
(d) $ \displaystyle 3qE\sqrt{a^2 + b^2} $
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Ans: (b)
Sol: Here , P (a, b, 0) & S (0, 0, 0)
$\displaystyle \vec{PS} = (0\hat{i} + 0\hat{j} + 0\hat{k})-(a\hat{i} + b\hat{j} + 0\hat{k})$
$ \displaystyle = – (a\hat{i} + b\hat{j}) $
Electric field
$ \displaystyle \vec{E} = E\hat{i} $
Work done by the field
$ \displaystyle = q E\hat{i}. (-a\hat{i} – b\hat{j}) $
= – q E a