Radius of curvature 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 radius of curvature of the particle’s orbit is determined by the mass, speed, and charge of the particle as well as by the magnetic flux density.

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 11.4.2.

radius_of_curvature¶

radius_of_curvature of the particle’s orbit.

Symbol:: r
Latex:: \(r\)
Dimension:: length

mass¶

mass of the particle.

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

speed¶

speed of the particle.

Symbol:: v
Latex:: \(v\)
Dimension:: velocity

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¶

r = m * v / (q * B)

Latex:: \[r = \frac{m v}{q B}\]