Charge Q is given a displacement vec r = ahat{i} + bhat{j} in an electric field vec E = E₁hat{i} +

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2. Electric Potential and Capacitance

easy

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

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

$Q\sqrt {{{({E_1}a)}^2} + {{({E_2}b)}^2}} $

$Q({E_1} + {E_2})\sqrt {{a^2} + {b^2}} $

$Q\sqrt {({E_1}^2 + {E_2}^2)} \sqrt {{a^2} + {b^2}} $

Solution

${\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)$

Standard 12

Physics

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hard

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

Solution

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