Skip to content

Biot-Savart Law

Source lecture(s): SC134 Lec9-10

Intuition

Every tiny current element paints a little contribution to the magnetic field, just like Coulomb's law for charge.

Formal Definition

\[d\vec{B} = \frac{\mu_0}{4\pi}\frac{i\,d\vec{l}\times\hat{r}}{r^2}\]

Mathematical Formulation

Integration over wire replaces \(i\,d\vec{l}\) with \(J\,d\vec{A}\) for volume currents.

Derivation

Empirical law from Oersted and Biot-Savart experiments; superposition yields integral form.

Worked Example

Center of circular loop radius \(R\): \(B = \mu_0 i/(2R)\).

Common Mistakes

  • Omitting \(\times\hat{r}\) cross product.
  • Integrating without projecting angle correctly.

Quiz

Q1. What symmetry makes Biot-Savart easiest?

Answer

Circular or straight segments.