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Q.

A point charge q moves from ‘P’ to ‘S’ along path PQRS in a uniform electric field E directed parallel to positive X-axis. The coordinates of the points P,Q, R and S are (a, b, 0), (2a, 0, 0), (0, -b, 0) and (0, 0, 0) respectively. The work done by field in the above process is given by

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a

– qEa

b

qEa

c

$qEa \sqrt{2}$

d

$qE \sqrt{(2 a)^{2} + b^{2}}$

answer is B.

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Detailed Solution

$\vec{E} = E \hat{i}; \vec{r} = - a \hat{i} - b \hat{j}; W = \vec{F} \cdot \vec{r}$

$W = q \vec{E} \cdot \vec{r} = qE \hat{i} \cdot (- a \hat{i} - b \hat{j}) = - Eqa$

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