Magnetic field

The magnetic field $⃗ 𝐁$ is an abstract pseudovector which describes how magnetic forces will act upon a moving test charge

⃗ 𝐅 𝑄 = ⃗ 𝐯 \times ⃗ 𝐁

as described by the Lorentz force law. The magnetic field follows the Principle of Superposition, so the effects of different sources may be combined easily.

Calculation

It follows from Maxwell's equations that

⃗ 𝐁 (⃗ 𝐫) = 𝜇 0 4 𝜋 ∭ ℝ 3 ⃗ 𝐉 (⃗ 𝐫') \times ˆ 𝔯 𝔯 2 𝑑 𝜏'

although historically this result is derived from consideration of the Biot-Savart Law.

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