The displacement of a charge $Q$ in the electric field $E = {e_1}\hat i + {e_2}\hat j + {e_3}\hat k$ is $\hat r = a\hat i + b\hat j$. The work done is
A$Q(a{e_1} + b{e_2})$
B$Q\sqrt {{{(a{e_1})}^2} + {{(b{e_2})}^2}} $
C$Q({e_1} + {e_2})\sqrt {{a^2} + {b^2}} $
D$Q(\sqrt {e_1^2 + e_2^2)} \;(a + b)$
Medium
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A$Q(a{e_1} + b{e_2})$
a (a) By using $W = Q\,(\overrightarrow E .\Delta \overrightarrow {r\,} )$
$W = Q\,[({e_1}\hat i + {e_2}\hat j + {e_3}\hat k).(a\hat i + b\hat j)] = Q\,({e_1}a + {e_2}b)$
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