👉 Thomson's Math, also known as Thomson's Theorem or Thomson's Relation, is a fundamental principle in electromagnetism that describes the behavior of magnetic fields generated by current-carrying conductors. It states that the magnetic field \( \mathbf{B} \) at a point in space due to a current \( I \) flowing through a wire is proportional to the current and inversely proportional to the distance from the wire, with the proportionality constant depending on the geometry of the current distribution. Specifically, \( \mathbf{B} \) is given by \( \mathbf{B} = \frac{\mu_0 I}{2\pi r} \hat{r} \), where \( \mu_0 \) is the permeability of free space, \( I \) is the current, \( r \) is the distance from the wire, and \( \hat{r} \) is the unit vector in the direction from the wire to the point. This theorem is crucial for calculating magnetic fields in various practical applications, from designing electrical circuits to understanding the behavior of motors and generators.
