Cylindrical symmetry

Definition

Cylindrical symmetry occurs when an object or system remains invariant under rotations about a central axis. It is commonly used in the context of electric fields and charge distributions.

5 Must Know Facts For Your Next Test

1. In cylindrical symmetry, the electric field depends only on the radial distance from the axis, not on the angular position or height along the axis.
2. Gauss's Law can be applied to systems with cylindrical symmetry to simplify the calculation of electric fields.
3. A common example of cylindrical symmetry is an infinitely long charged wire, where the electric field at any point depends only on its distance from the wire.
4. For a cylindrical Gaussian surface, Gauss's Law states that $\oint \mathbf{E} \cdot d\mathbf{A} = \frac{q_{enc}}{\epsilon_0}$, where $q_{enc}$ is the charge enclosed by the surface.
5. The use of cylindrical coordinates (r, θ, z) is particularly useful for solving problems involving cylindrical symmetry.

Review Questions

• What is meant by cylindrical symmetry in terms of electric fields?
• How does Gauss's Law simplify calculations for systems with cylindrical symmetry?
• Provide an example of a physical system that exhibits cylindrical symmetry.

Related terms

Gaussian Surface: An imaginary closed surface used in Gauss's Law to calculate flux and relate it to enclosed charge.

Electric Flux: $$\Phi_E = \oint \mathbf{E} \cdot d\mathbf{A}$$; A measure of the number of electric field lines passing through a given area.

Radial Distance: The distance from a central axis to a point in space within a system exhibiting cylindrical symmetry.