Question

The electric flux of a surface is maximum, when

Answer 1

Electric flux:

1. The total number of lines of force passing through a surface is called electric flux.
2. The SI unit of electric flux is $\mathrm{volt}\mathrm{metres}(\mathrm{V}\mathrm{m})$ or newton-meters squared per coulomb $(\mathrm{N}{\mathrm{m}}^2{\mathrm{C}}^{-1})$.
3. Electric field lines are designed, to begin with, positive charges and conclude with negative charges.
4. The total flux associated with the surface can be expressed as,

$$\begin{gathered} \Phi E=E\cdot A \\ =EAcos\theta \end{gathered}$$

Where, $E$ is the magnitude of the electric field, $A$ is the area of the surface, $\theta$ is the angle between the electric field lines and the normal to $A$.

Explanation:

1. Gauss’ Law makes use of the concept of “flux”. Flux is always defined based on the surface, $A$ and the vector field, $\overrightarrow{E}$.
2. If the surface is perpendicular to the field (left panel), and the field vector is thus parallel to the vector, $\overrightarrow{A}$ , then the flux through that surface is maximum.
3. If the surface is parallel to the field (right panel), then no field lines cross that surface, and the flux through that surface is zero.
4. If the surface is rotated with respect to the electric field, as in the middle panel, then the flux through the surface is between zero and the maximum value.

Therefore, the electric flux of a surface is maximum when the area vector is parallel to the direction of the electric field.