Question
Charge $Q$ is given a displacement $\vec r = a\hat i + b\hat j$ in an electric field $\vec E = E_1\hat i + E_2\hat j$ . The work done is
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Answer
${\rm{W}} = \overrightarrow {\rm{F}} \cdot \overrightarrow {\rm{r}} = {\rm{Q}}\overrightarrow {\rm{E}} \cdot \overrightarrow {\rm{r}} $
$ = {\rm{Q}}\left( {{{\rm{E}}_1}\widehat {\rm{i}} + {{\rm{E}}_2}\widehat {\rm{j}}} \right) \cdot ({\rm{a}}\widehat {\rm{i}} + {\rm{b}}\widehat {\rm{j}}) = {\rm{Q}}\left( {{{\rm{E}}_1}{\rm{a}} + {{\rm{E}}_2}{\rm{b}}} \right)$
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