A charged particle entering a uniform magnetic field at right angles moves in a circle because
Electromagnetism - OCR A-Level Physics
- A charged particle entering a uniform magnetic field at right angles moves in a circle because the force is always perpendicular to the velocityThe rate of change of displacement. A vector quantity. Measured in m s⁻¹..
- The magnetic force provides the centripetal forceThe resultant force directed towards the centre of a circular path that causes an object to move in a circle. It is not a separate force but the net force providing circular motion.: $BQv = mv^{2}/r$.
- Rearranging gives the radius of the circular path.
$$r = \frac{mv}{BQ}$$
- Faster particles trace larger circles (r ∝ v).
- More massive particles trace larger circles (r ∝ m).
- Stronger fields produce tighter circles (r ∝ 1/B).
- This is the principle behind the cyclotronA particle accelerator that uses a magnetic field to bend charged particles in a spiral and an electric field to accelerate them. and mass spectrometerAn instrument that separates ions by mass-to-charge ratio using electric and magnetic fields..
Common Mistake
MEDIUM
Wrong: The particle spirals inward because the magnetic force accelerates it.
Right: The magnetic force does no work, so the speed and kinetic energyThe capacity to do work. Measured in joules (J).The energyThe capacity to do work. Measured in joules (J). an object possesses due to its motion. are constant. The radius stays constant and the path is a perfect circle (not a spiral), unless energyThe capacity to do work. Measured in joules (J). is lost by other means.
Right: The magnetic force does no work, so the speed and kinetic energyThe capacity to do work. Measured in joules (J).The energyThe capacity to do work. Measured in joules (J). an object possesses due to its motion. are constant. The radius stays constant and the path is a perfect circle (not a spiral), unless energyThe capacity to do work. Measured in joules (J). is lost by other means.