A cube has sides of length \( L \). It is placed with one corner at the origin as shown in figur...

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A cube has sides of length \( L \). It is placed with one corner at the origin as shown in figure. The electric field is uniform and given by \( \mathbf{E}=-B \hat{\mathbf{i}}+C \hat{\mathbf{j}}-D \hat{\mathbf{k}} \), where \( B, C \) and \( D \) are positive constants.
(a) Find the electric flux through each of the six cube faces \( S_{1}, S_{2}, S_{3}, S_{4}, S_{5} \) and \( S_{6} \).
(b) Find the electric flux through the entire cube.
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