First slide

Gauss's law and its applications

Question

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

Moderate

Solution

$F l u x, φ = \vec{E} . \vec{A} A r e a v e c t o r i s p e r p e n d i c u l a r l y a w a y f r o m p l a n e s u r f a c e i . e A r e a p e r p e n d i c u l a r t o X Y p l a n e i s Z a x i s G i v e n : \vec{A} = (100 \hat{k}), \vec{E} = \hat{i} + \sqrt{2} \hat{j} + \sqrt{3} \hat{k} ∴ φ = (\hat{i} + \sqrt{2} \hat{j} + \sqrt{3} \hat{k}) . (100 \hat{k}) = 100 \sqrt{3} = 173.2$

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