# Biot-Savart Law

## Table of Contents

The Biot-Savart Law describes the magnetic field generated by a constant electric current in magneto-statics. It is as follows:

$$ B(r) = \frac{\mu_0}{4\pi} \int \frac{I d\ell \times r’}{|r’|^3} $$

Where

- \( \small B(r) \) is the magnetic field at point \( \small r \),
- \( \small \mu_0 \) is the permeability of free space,
- \( \small I \) is the current,
- \( \small d\ell \) is an infinitesimal current element,
- \( \small r’ = r - \ell \) is the displacement vector from the current element to the observation point, and
- \( \small |r’| \) is the magnitude of \( \small r’ \).

In other words, to actually use the law, you choose a point r where you want to know the magnetic field, you mathematically describe the geometry of the current-carrying wire such that you know the magnitude and direction of the vector between the current element and the point r, and then you integrate over the entire wire’s elements to get the total magnetic field at point r.