Spherical symmetry

Definition

Spherical symmetry refers to a system where physical properties are invariant under any rotation about the center point. In such a system, the properties depend solely on the radial distance from the center.

5 Must Know Facts For Your Next Test

1. In systems with spherical symmetry, Gauss's Law simplifies calculations of electric fields because the electric field magnitude is constant at a given radius.
2. The electric flux through a spherical surface depends only on the total charge enclosed, not on how that charge is distributed within the sphere.
3. For a point charge, the electric field exhibits spherical symmetry and falls off as $\frac{1}{r^2}$ with distance $r$ from the charge.
4. In spherical symmetry, Gaussian surfaces are typically chosen to be spheres centered at the source of symmetry to exploit this property.
5. Spherical symmetry is crucial for solving problems involving uniformly charged spheres or spherical shells.

Review Questions

• How does Gauss's Law simplify in systems with spherical symmetry?
• Why is a Gaussian surface often chosen to be a sphere in problems involving spherical symmetry?
• What happens to the electric field as you move away from a point charge in a system exhibiting spherical symmetry?

Related terms

Gauss's Law: A fundamental law stating that the net electric flux through any closed surface is equal to $\frac{1}{\epsilon_0}$ times the total charge enclosed within that surface.

Electric Flux: A measure of the quantity of electricity being pushed through an area; mathematically defined as $\Phi_E = \mathbf{E} \cdot \mathbf{A}$.

Radial Distance: The straight-line distance from a specific central point (often an origin) to another point in space.