Electric flux through a surface of area 100 m2 lying in the x, y plane is (in V-m) if E→=i^+2 j^+3 k^

Electric flux through a surface of area 100 m² lying in the x, y plane is (in V-m) if $\vec{E} = \hat{i} + \sqrt{2} \hat{j} + \sqrt{3} \hat{k}$

A
100
B
141.4
C
173.2
D
200

Solution:

Area of surface $\vec{A} = 100 m^{2} \hat{k}$ (xy plane) and

$\begin{array}{l} \vec{E} = (\hat{i} + \sqrt{2} \hat{j} + \sqrt{3} \hat{k}) \frac{V}{m} \\ \Rightarrow ϕ = \vec{E} \cdot \vec{A} = (\vec{E} = \hat{i} + \sqrt{2} \hat{j} + \sqrt{3} \hat{k}) \cdot 100 \hat{k} \\ = 0 + 0 + \sqrt{3} \times 100 = 173 .2 Vm \end{array}$

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