Gaussian surface

Definition

A Gaussian surface is an imaginary closed surface used in Gauss's Law to calculate the flux of an electric field. The choice of Gaussian surface simplifies the calculation of electric fields due to symmetric charge distributions.

5 Must Know Facts For Your Next Test

1. The total electric flux through a Gaussian surface is proportional to the enclosed charge.
2. Gauss's Law is given by $\Phi_E = \frac{Q_{\text{enc}}}{\varepsilon_0}$ where $\Phi_E$ is the electric flux, $Q_{\text{enc}}$ is the enclosed charge, and $\varepsilon_0$ is the permittivity of free space.
3. A spherical Gaussian surface is often used for point charges due to its symmetry.
4. For an infinitely long line of charge, a cylindrical Gaussian surface simplifies calculations.
5. When using a planar symmetry, the most effective Gaussian surface is a pillbox shape.

Review Questions

• What role does symmetry play in choosing an appropriate Gaussian surface?
• How does Gauss's Law relate the electric flux through a Gaussian surface to the enclosed charge?
• Why might you choose a spherical Gaussian surface for a point charge?

Related terms

Electric Flux: The measure of the quantity of electricity flowing through a given area, typically calculated as $\Phi_E = \mathbf{E} \cdot \mathbf{A}$.

Permittivity of Free Space (\varepsilon_0): A constant that describes how much electric field (force per unit charge) is 'permitted' in free space, with a value approximately equal to $8.85 \times 10^{-12} \, \text{F/m}$.

Symmetry: The property that allows simplification in physical laws and calculations by exploiting uniformity in spatial configurations such as spherical, cylindrical, or planar symmetry.