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# The electric field in a region is given by $\;\overrightarrow{E}=\alpha \hat{i}+\beta \hat{j}\;.$ Here $\;\alpha\; and \; \beta\;$ are constants . The net flux through a square are of side l parallel to y - z plane

$(a)\;\alpha\;l^2\qquad(b)\;\beta\;l^2\qquad(c)\;(\alpha+\beta)\;l^2\qquad(d)\;\large\frac{\alpha+\beta}{2}\;l^2$

Answer : (a) $\;\alpha\;l^2$
Explanation : A square are of side l parallel to y - z plane in vector form can be written as
$\overrightarrow{S}=l^2\;\hat{i}$
$\overrightarrow{E}=\alpha \hat{i}+\beta \hat{j}$
$\phi=\overrightarrow{E}\;.\overrightarrow{S}$
$\phi=(\alpha \hat{i}+\beta\hat{j})\;.(l^2\;.\hat{i})$
$\phi=\alpha\;l^2\;.$