Biot-Savart Law

The Biot-Savart law can be used to determine the Magnetic Field from a system of moving Charges, similar to how Coulomb’s Law gives the Electrostatic Force on a system of stationary charges.

Definition §

Assume we have a moving charge $q$ with velocity $\vec{v}$. If we were to calculate the magnetic field at a point $r$ distance away, the force is given by:

Formula §

$$\vec{B}=\frac{{\mu }_0}{4\pi }\frac{q}{r^2}(\vec{v}\times \hat{u})$$

• $\vec{B}$ = Magnetic Field (in $T$ or $N/Am$)
• ${\mu }_0$ = Permeability of free space $\approx 1.26\times 10^{-}6$ (in $N/A^2$)
• $q$ = Charge of the (moving) charged object generating magnetic field
• $r$ = Distance from charged object
• $\vec{v}$ = Velocity of charged object
• $\vec{u}$ = Direction vector from charged particle