As per this diagram a point charge +q is placed at the origin O. Work done in taking another point charge –Q from the point A (coordinates (0, a)) to another point B (coordinates (a, 0)) along the straight path AB is

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$(\frac{- q Q}{4 π ε_{0} a^{2}}) \sqrt{2} a$

$(\frac{q Q}{4 π ε_{0} a^{2}}) \frac{a}{\sqrt{2}}$

$(\frac{q Q}{4 π ε_{0} a^{2}}) \sqrt{2} a$

answer is A.

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Detailed Solution

$V_{A} = \frac{1}{4 π \in_{0}} . \frac{q}{a}, V_{B} = \frac{1}{4 π \in_{0}} . \frac{q}{a}$

$W_{A \to B} = - Q (V_{B} - V_{A}) = 0$

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