The Microscopic Source of Magnetism
The Biot-Savart Law is the most fundamental equation for calculating magnetic fields. It describes the magnetic field ($B$) generated by a tiny segment of current-carrying wire.
While Ampere's Law is easier to use for symmetrical shapes (like long wires or solenoids), the Biot-Savart Law can calculate the magnetic field for any wire shape, no matter how complex. This specific calculator focuses on the simplest case: the field generated by a single moving point charge.
The Inverse-Square Law of Magnetism
Like gravity and electric force, the magnetic field from a point source follows an inverse-square law. If you double your distance from a moving charge, the magnetic field it generates drops to one-fourth. Furthermore, the field depends on the sine of the angle; the field is strongest perpendicular to the motion and zero directly in front of or behind the charge.
The Formula
Example Calculation
A proton ($q = 1.6 \times 10^{-19} , \text{C}$) is moving at $10^6 , \text{m/s}$. Find the field at a point $1 , \text{mm}$ ($0.001 , \text{m}$) away, perpendicular to the motion ($ heta = 90^\circ$).
- Constants: $\mu_0 / 4\pi = 10^{-7}$.
- Calculate: $10^{-7} \times (1.6 \times 10^{-19} \times 10^6 \times \sin(90^\circ)) / (0.001)^2 = 1.6 \times 10^{-14} , \text{T}$.
The magnetic field from a single moving proton is incredibly tiny.