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Question

(A) The electric flux $\phi$ through a surface is defined by the dot product of the electric field vector $\vec{E}$ and the area vector $\vec{A}$.Give

Vedclass · Accepted Answer

$a \pi R^2$

Vedclass · Answer

(A) The electric flux $\phi$ through a surface is defined by the dot product of the electric field vector $\vec{E}$ and the area vector $\vec{A}$.Given $\vec{E} = a \hat{i} + b \hat{j} + c \hat{k}$ and $\vec{A} = \pi R^2 \hat{i}$.$\phi = \vec{E} \cdot \vec{A} = (a \hat{i} + b \hat{j} + c \hat{k}) \cdot (\pi R^2 \hat{i})$.Since $\hat{i} \cdot \hat{i} = 1$,$\hat{i} \cdot \hat{j} = 0$,and $\hat{i} \cdot \hat{k} = 0$,we get:$\phi = a \cdot \pi R^2 = a \pi R^2$.

The electric field in a region is uniform and is given by $\vec{E} = a \hat{i} + b \hat{j} + c \hat{k}$. The electric flux associated with a surface of area $\vec{A} = \pi R^2 \hat{i}$ is:

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