First slide

Gauss's law and its applications

Question

The electric field in a region is given by $\vec{E} = \frac{3}{5} E_{0} \hat{i} + \frac{4}{5} E_{0} \hat{j}$ with $E_{0} = 2 \times 10^{3} N / C$ . Find the flux of this field through a rectangular surface of area $0.2 m^{2}$ parallel to $y - z$ plane in $N - m^{2} C^{- 1}$

NA

Solution

$\vec{E} = \frac{3}{5} (2 \times 10^{3}) \hat{i} + \frac{4}{5} (2 \times 10^{3}) \hat{j} = 1200 \hat{i} + 1600 \hat{j} \vec{A} = (0.2 \hat{i}) m^{2} F l u x (φ) = \vec{E} . \vec{A} = (1200 \hat{i} + 1600 \hat{j}) . (0.2 \hat{i}) = 240 N - m^{2} / C$

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