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# Charge Q is given displacement $\overrightarrow {r} = a\hat i + b \hat j$ in electric field $\overrightarrow {E}= E_1 \hat i +E_2 \hat j .$ work done is :

$(A)\;Q \sqrt {E_1 ^2 +E_2 ^2 } \sqrt {a^2 +b^2} \\ (B)\;Q(E_1 +E_2) \sqrt {a^2 +b^2} \\ (C)\; Q(E_1 a +E_2 b) \\ (D)\;None$

$w= \overrightarrow {F} . \overrightarrow {r}$
$\quad= Q \overrightarrow {E} . \overrightarrow {r}$
$\quad = Q (E_1 \hat i + E_2 \hat j ). (a \hat i +b \hat j)$
$\quad= Q(E_1 a +E_2 b)$
Hence C is the correct answer.