A cube of side l has one corner at the origin of coordinates and extends along the positive `x-,y- and z-axes.` Suppose that the electric field in this region is given by `vec E = (a+by)hatj`. Determine the charge inside the cube (a and b are some constants).

Explanation

To determine the charge inside the cube given the electric field \( \vec{E} = (a + by) \hat{j} \), we will use Gauss's law, which states:

\[ \Phi_E = \frac{Q_{\text{enc}}}{\epsilon_0} \]

where \( \Phi_E \) is the electric flux through a closed surface, \( Q_{\text{enc}} \) is the charge enclosed within that surface, and \( \epsilon_0 \) is the permittivity of free space.

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