Question

What is Gauss's theorem in electrostatics?

• A. ϕ=q/ε₀
• B. ϕ= ε₀/q
• C. q = ε₀/ϕ
• D. $ε₀=ϕ/q$

Answer 1

Answer:

A. ϕ=q/ε₀

• Gauss's Law (also known as Gauss's Flux Theorem) establishes the relationship between the distribution of electric charge and the resulting electric field.

• The law states that the total electric flux passing through any closed surface (often called a Gaussian surface) is equal to 1/ε₀ times the total net charge enclosed by that surface.

• Mathematically expressed as: Φ = ∮ E · dA = Q_enclosed / ε₀, where Φ is the electric flux, E is the electric field, dA is an area element vector, Q_enclosed is the total charge inside the surface, and ε₀ is the permittivity of free space.

• Dependence on Geometry: The law is valid for any arbitrary closed surface, regardless of its shape or size.

• Source Independence: The electric field E on the right side of the equation is the total electric field produced by all charges, both inside and outside the Gaussian surface. However, only charges inside the surface contribute to the flux.

• Relation to Coulomb's Law: Gauss's Law is essentially a restatement of Coulomb's Law, but expressed in a form that makes calculations for highly symmetric charge distributions (like spheres, cylinders, or infinite planes) much simpler.