Q. In a region of space, the electric field is given by $ \displaystyle \vec{E} = 8\hat{i} + 4\hat{j} + 3\hat{k} $ . The electric flux through a surface of area 100 units in the xy plane is

(a) 800 units

(b) 300 units

(c) 400 units

(d) 1500 units

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Ans: (b)

Sol: $ \displaystyle \vec{E} = 8\hat{i} + 4\hat{j} + 3\hat{k} $

Area vector is

$ \displaystyle \vec{A} = 100 \hat{k} $ (As it perpendicular to XY Plane)

Electric flux

$ \displaystyle \phi = \vec{E} . \vec{A} $

$ \displaystyle \phi = (8\hat{i} + 4\hat{j} + 3\hat{k}) . (100 \hat{k}) $

= 300 unit