Discussion
A uniformly charged cube of side one cm having surface charge density of 8.85 μC cm-2is placed inside a hollow metal sphere. The total flux emerging out of the sphere in Nm2C-1 is (ε0 = 8.85 x 10-12 C2N-1m-2)
Answer: E
The flux is \(6 \times 10^{6}\) N m2 C-1.
The cube has 6 faces of 1 cm2, so its total charge is \(q = 8.85\ \mu\text{C cm}^{-2} \times 6\ \text{cm}^{2} = 53.1\ \mu\text{C}\). The uncharged metal sphere does not change the net enclosed charge, so by Gauss's law:
\[ \begin{aligned} \Phi &= \frac{q}{\varepsilon_0} = \frac{53.1 \times 10^{-6}}{8.85 \times 10^{-12}} \\ &= 6 \times 10^{6} \end{aligned} \]
Using one face only gives \(1 \times 10^{6}\); the other values do not follow from the cube's six faces.
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