Forest UCM PnCP
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Charged Particle in uniform B-Field
Consider a charged particle moving the x-y plane in the presence of a uniform magnetic field with field lines in the z-dierection.
- \vec{v} = v_x \hat i + v_y \hat j
- \vec{B} = B \hat k
- Lorentz Force
- \vec{F} = q \vec{E}q\vec{v} \times \vec{B}
- Note
- the work done by a magnetic field is zero if the particle's kinetic energy (mass and velocity) don't change.
- W = \Delta K.E.
No work is done on a charged particle force to move in a fixed circular orbit by a magnetic field (cyclotron)