Consider an electric field $¯ ¯¯ ¯ E = E_{0}^x$ , where $E_{0}$ is a constant. The flux through the shaded area (as shown in the figure) due to this field is:

2 E_{0} a^{2}

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\sqrt{2} E_{0} a^{2}

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E_{0} a^{2}

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\frac{E_{0} a^{2}}{\sqrt{2}}

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Solution

The correct option is B $E_{0} a^{2}$
$F l u x t h r o u g h a r e a = E l e c t r i c f i e l d \times A r e a p r o j e c t e d$
$ϕ = E A c o s 45^{o}$
$= E_{0} (\sqrt{2} a^{2}) \times \frac{1}{\sqrt{2}}$
$= E_{0} a^{2}$

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Consider an electric field ¯¯¯¯E=E0^x, where E0 is a constant. The flux through the shaded area (as shown in the figure) due to this field is:

The correct option is B E0a2Flux through area=Electric field×Area projectedϕ=EAcos45o =E0(√2a2)×1√2 =E0a2

Consider an electric field $¯ ¯¯ ¯ E = E_{0}^x$ , where $E_{0}$ is a constant. The flux through the shaded area (as shown in the figure) due to this field is:

The correct option is B $E_{0} a^{2}$
$F l u x t h r o u g h a r e a = E l e c t r i c f i e l d \times A r e a p r o j e c t e d$
$ϕ = E A c o s 45^{o}$
$= E_{0} (\sqrt{2} a^{2}) \times \frac{1}{\sqrt{2}}$
$= E_{0} a^{2}$