Charge Q is given a displacement r = a i + b j in an electric fie… - Vidyadip

MCQ

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

✓
$Q({E_1}a + {E_2}b)$
B
$Q\sqrt {{{({E_1}a)}^2} + {{({E_2}b)}^2}} $
C
$Q({E_1} + {E_2})\sqrt {{a^2} + {b^2}} $
D
$Q\sqrt {({E_1}^2 + {E_2}^2)} \sqrt {{a^2} + {b^2}} $

✓

Answer

Correct option: A.

$Q({E_1}a + {E_2}b)$

a
${\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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