Period of rotation of charged particle in magnetic field¶

When a charged particle enters a magnetic field, it experiences an electromagnetic force upon itself. In the absence of the electric field, the particle starts moving in a circular orbit. The period of the particle’s rotation is determined by the mass and charge of the particle as well as by the magnetic field and it does not depend on the particle speed.

Conditions:

The particle’s speed and the magnetic field are perpendicular to each other.
The magnetic field is uniform.
The electric field is zero.

Links:

Physics LibreTexts, formula 11.4.3.

period¶

period of the particle’s rotation.

Symbol:: T
Latex:: \(T\)
Dimension:: time

mass¶

mass of the particle.

Symbol:: m
Latex:: \(m\)
Dimension:: mass

charge¶

charge of the particle.

Symbol:: q
Latex:: \(q\)
Dimension:: charge

magnetic_flux_density¶

Magnitude of magnetic_flux_density.

Symbol:: B
Latex:: \(B\)
Dimension:: magnetic_density

law¶

T = 2 * pi * m / (q * B)

Latex:: \[T = \frac{2 \pi m}{q B}\]