Formula explainer. Open the full deep dive
Electromagnetism Formula

What is Ampere's Law?

The line integral of the magnetic field around any closed loop equals μ₀ times the total current passing through the loop.

Formula: \oint \vec{B}\cdot d\vec{l} = \mu_0 I_{enc}

Plain-English Meaning

The line integral of the magnetic field around any closed loop equals μ₀ times the total current passing through the loop.

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

Deeper Explanation

The line integral of the magnetic field around any closed loop equals μ₀ times the total current passing through the loop.

Worked Example

Problem: Use Ampere's law to find B inside a long solenoid with n turns/m carrying current I.

  • Choose a rectangular loop: length L inside, length L outside solenoid.
  • B outside solenoid ≈ 0; field inside is uniform and parallel to axis.
  • ∮B⃗·dl⃗ = B·L = μ₀(nL)I
  • B = μ₀nI

Result: B = μ₀nI inside the solenoid

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.