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Electromagnetism Formula

What is Gauss's Law?

The total electric flux through any closed surface equals the enclosed charge divided by ε₀.

Formula: \oint \vec{E}\cdot d\vec{A} = \frac{Q_{enc}}{\varepsilon_0}

Plain-English Meaning

The total electric flux through any closed surface equals the enclosed charge divided by ε₀.

Keep charge, field, potential, and current distinct. That single habit fixes a large fraction of electromagnetism errors.

Deeper Explanation

The total electric flux through any closed surface equals the enclosed charge divided by ε₀.

Worked Example

Problem: Use Gauss's law to find E outside a uniformly charged sphere (total charge Q, radius R) at r > R.

  • Choose a concentric spherical Gaussian surface of radius r.
  • By symmetry, E is constant and radial on this surface.
  • Gauss's law: E × 4πr² = Q/ε₀
  • E = Q/(4πε₀ r²) = kQ/r².

Result: E = kQ/r² (same as a point charge)

At A Glance

Category: Electromagnetism

Levels covered:

Best use: Start with the formula meaning, then move to the worked example and quiz so the equation turns into a tool instead of a memorised line.