Magnetic force

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

For point charges, the magnitude of the magnetic force is

$\displaystyle \left \lvert \vec{F}_{\text{M}} \right \rvert = q v \left \lvert \vec{B} \right \rvert \sin{\theta}$,

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

$\displaystyle \left \lvert \vec{F}_{\text{M}} \right \rvert = \left \lvert \vec{B} \right \rvert I L \sin{\theta}$,

where $\displaystyle \vec{B}$ and $\displaystyle \theta$ are the same as before, and where $\displaystyle I$ is the current in amperes (A) and $\displaystyle L$ 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.