A charge 'Q' $\mu$ C is placed at the centre of a cube. The flux through one face and two opposite faces of…

A charge 'Q' $\mu$ C is placed at the centre of a cube. The flux through one face and two opposite faces of the cube is respectively
  1. $\frac{\mathrm{Q}}{6 \epsilon_{0}} \mu \mathrm{Vm}, \quad \frac{\mathrm{Q}}{3 \epsilon_{0}} \mu \mathrm{Vm}$
  2. $\frac{\mathrm{Q}}{12 \epsilon_{0}} \mu \mathrm{Vm}, \quad \frac{\mathrm{Q}}{\epsilon_{0}} \mu \mathrm{Vm}$
  3. $\frac{\mathrm{Q}}{6 \epsilon_{0}} \mu \mathrm{Vm}, \quad \frac{\mathrm{Q}}{2 \epsilon_{0}} \mu \mathrm{Vm}$
  4. $\frac{\mathrm{Q}}{12 \epsilon_{0}} \mu \mathrm{Vm}, \quad \frac{\mathrm{Q}}{3 \epsilon_{0}} \mu \mathrm{Vm}$

Solution

By using Gauss's Law. It is given as $\Phi=\oint \vec{E} \cdot d \vec{s}=\frac{q}{\epsilon_{0}}$ Now, the flux passing through all the six surfaces would be $\Phi=6 \phi=\frac{q}{\epsilon_{0}}$ And the flux passing through each surface would be $\phi=\frac{q}{6 \in_{0}}$

Asked in: MHT CET 2020 (20 Oct Shift 1)

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