Magnetic force

A magnetic field can cause charges (e⁻, p⁺, or ions) to move due to a magnetic force, denoted by ${\overrightarrow{F}}_{\text{M}}\text{.}$ We usually figure out the magnitude and the direction of the force separately.

For point charges, the magnitude of the magnetic force is

$\left|{\overrightarrow{F}}_{\text{M}}\right|=qv\left|\overrightarrow{B}\right|\sin \theta \text{,}$

where $q$ is the charge in coulombs (C), $v$ is the speed of the particle in metres per second (m/s), $\overrightarrow{B}$ is the magnetic field in teslas (T), and $\theta$ is the angle between the conventional current and the magnetic field.

To get the direction, we once again use the right-hand rule. Your fingers (flat, not curled) point in the direction of the magnetic field (the north pole being at your finger tips); your thumb points in the direction of the conventional current (positive to negative—if it’s an electron that’s moving, the current is in the direction opposite to the particle velocity); and your palm, if you imagine that there is an arrow perpendicular to it going out from the centre, represents the magnetic force.

It works a bit differently for conductors. We get the magnitude of the magnetic force for straight conductors with

$\left|{\overrightarrow{F}}_{\text{M}}\right|=\left|\overrightarrow{B}\right|IL\sin \theta \text{,}$

where $\overrightarrow{B}$ and $\theta$ are the same as before, and where $I$ is the current in amperes (A) and $L$ is the length of the conductor inside the magnetic field in metres (m). The right-hand rule works the same way that it does for point charges.