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  4. An electric field given by vecE=4 hati-(3 y2+2) hatj pierces Gaussian's cube of side 1 m placed at origin such that its three sides represents x, y and z axes. The net charge enclosed within the cube is given by -n e 0. Find the value of n.

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Q. An electric field given by $\vec{E}=4 \hat{i}-\left(3 y^{2}+2\right) \hat{j}$ pierces Gaussian's cube of side $1 m$ placed at origin such that its three sides represents $x, y$ and $z$ axes. The net charge enclosed within the cube is given by $-n e _{0}$. Find the value of $n$.Physics Question Image

Electric Charges and Fields

Solution:

Net flux in $x$-direction $=0$
Net flux in $y$-direction $=-A\left[3(1)^{2}+2\right]+A[3(0)+2]$
$\Rightarrow q=-3 \varepsilon_{0} \,\,\left(\right.$ As $\left.A=1 m ^{2}\right)$