Fields - Magnetic Fields

Magnetic fields (denoted by $B$) are vector fields that exert forces on moving charges and current-carrying conductors. The SI unit for magnetic field strength is the Tesla ($T$).

Magnetic field lines represent the direction and magnitude of the field. They always point from the North pole to the South pole outside a magnet and their density indicates the field strength.

A point charge $q$ moving with velocity $v$ in a magnetic field $B$ experiences a force $F = qvB \sin\theta$, where $\theta$ is the angle between the velocity and the magnetic field vectors.

A straight conductor of length $L$ carrying a current $I$ in a magnetic field experiences a force $F = BIL \sin\theta$.

The direction of the magnetic force is determined by the Right-Hand Rule: for a positive charge, if the thumb points in the direction of velocity $v$ and the fingers in the direction of $B$, the palm points in the direction of the force $F$.

Since the magnetic force is always perpendicular to the velocity of a charged particle, it does no work and results in uniform circular motion with a radius $r = \frac{mv}{qB}$.

The magnetic field strength $B$ at a distance $r$ from a long straight current-carrying wire is given by $B = \frac{\mu_0 I}{2\pi r}$, where $\mu_0$ is the permeability of free space ($4\pi \times 10^{-7} \text{ T m A}^{-1}$).