Biot Savart Law

Magnetic Monopole

Steady Current

More realistically is the magnetic field created by a steady current. A steady current is the condition when the current does not change over time. More strictly, the current distribution should not change over time say for a volumetric current \(\partial \bvec J / \partial t = \bvec 0\)

\[ \bvec{B}(\bvec r) = \frac{\mu_0}{4\pi}\int\frac{\bvec I \times \bvec{\hat d}}{d^2}\mathrm dl = \frac{\mu_0}{4\pi}I \int\frac{\mathrm d\bvec{l} \times \bvec{\hat r}}{d^2} \]

• \(\mu_0\) : The constant of permeability of free space \(\mu_0 = 4\pi \times 10^{-7} \mathrm{N/A^2}\)

• \(\bvec d\) : Distance vector from \(\mathrm d \bvec l\) to \(\bvec r\)

Divergence

\[ \nabla \cdot \bvec B = 0 \]