Rankers Physics

Gauss's Law: Practice Problem & Solution

A charge $q$ is located at the centre of a cube. The electric flux through any face is: (2003)
$\frac{2\pi q}{6(4\pi\varepsilon_0)}$
$\frac{4\pi q}{6(4\pi\varepsilon_0)}$
$\frac{\pi q}{6(4\pi\varepsilon_0)}$
$\frac{q}{6(4\pi\varepsilon_0)}$

Solution Explained:

To solve this problem, we apply the core principles of Gauss's Law. Understanding the underlying formula is key to arriving at the correct answer below:

Total flux through the cube is $\frac{q}{\varepsilon_0}$ by Gauss's law. Since a cube has 6 identical faces, the flux through any one face is one-sixth of the total flux. Therefore, the flux through any face is $\frac{q}{6\varepsilon_0} = \frac{4\pi q}{6(4\pi\varepsilon_0)}$.

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