Circular motion in magnetic field
Equation
The magnetic component of the Lorentz force
$ F = q v B \sin \theta $ |
It is always perpendicular to the direction of movement leading to the particle moving in a circle (the speed is tangential to it and thus always orthogonal to the radius). The radius will have to be such that the magnetic force is equal to the centrifugal force so it will have to
$ m \displaystyle\frac{ v ^2}{ r }= q v B $ |
ID:(3229, 0)
Lorenz Law
Equation
The force
$ \vec{F} = q ( \vec{E} + \vec{v} \times \vec{B} )$ |
ID:(3219, 0)
Magnitude of the magnetic component of the Lorentz force
Equation
The magnetic component of the Lorentz force is
$ \vec{F} = q \vec{v} \times \vec{B} $ |
so with
its magnitude will be
$ F = q v B \sin \theta $ |
ID:(3873, 0)
Radius of the orbit in the magnetic field
Equation
Being the movement of an electric charge in a circular magnetic field satisfying the equality between the magnetic and centrifugal forces
$ m \displaystyle\frac{ v ^2}{ r }= q v B $ |
it will have that the radius of the orbit will be
$ r =\displaystyle\frac{ m v }{ q B }$ |
ID:(3874, 0)