Question

Define electric flux through a surface. Give the significance of a Gaussian surface. A charge outside a Gaussian surface does not contribute to total electric flux through the surface. Why?

Hint:

The electric flux through a surface is proportional to the charge enclosed by that surface, as per Gauss’s law.

Answer 1

The electric flux \( \Phi_E \) across a surface quantifies the electric field \( E \) passing through it. It is calculated as the product of the electric field strength \( E \), the surface area \( A \), and the cosine of the angle \( \theta \) between the electric field vector and the surface's normal vector: \[ \Phi_E = E \cdot A \cdot \cos(\theta) \] A Gaussian surface is a hypothetical closed surface employed in Gauss's law for electric flux calculations. Its importance lies in simplifying electric flux computations and, via Gauss's law, enabling the determination of electric fields generated by symmetrical charge arrangements. Charges situated outside a Gaussian surface have no effect on the net electric flux through it. This is because the electric field lines originating from external charges do not penetrate the surface, resulting in a zero net flux.