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  • In a region of space, the electric field is in the x-direction and is given by <img alt="\mathrm{\overrightarrow{E}=E_0 x \hat{i}}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7B

In a region of space, the electric field is in the x-direction and is given by \mathrm{\overrightarrow{E}=E_0 x \hat{i}}. consider an imaginary cubical volume of edge 'a' with edges parallel to the axes of coordinates. The charge inside the cube will be

Option: 1

\mathrm{E_0 a^3 }


Option: 2

\mathrm{\epsilon_0 E_0 a^3}


Option: 3

\mathrm{\epsilon_0 \epsilon_0^2 a^3}


Option: 4

\mathrm{\epsilon_0 E_0^3 a}


Answers (1)

best_answer

At \mathrm{x=0, E=0}
and \mathrm{x=a, E=E_0 a}
Total floux  \mathrm{\phi =0 \times a^2+E \times a^2=E_0 a \times a^2}

                  \mathrm{\phi =E a^3}    .....(1)
using gauss law.
                  \mathrm{ \phi=\frac{q}{G_0}}

                  \mathrm{ q=\phi \epsilon_0=E a^3 \epsilon_0}

Posted by

jitender.kumar

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