Moving Charges in a Magnetic Field
Physics: AQA A Level, topic 7.5.3
Force on a charged particle
A magnetic field will create a force on a charged particle. This is called the Lorentz force.
Lorentz force
- The Lorentz force always acts perpendicular to the velocity of a particle.
- This means that the force acts as a centripetal force.
- Particles in magnetic fields undergo circular motion.
Calculation
- We know that the centripetal force is given by
- If the particle is travelling in a magnetic field perpendicular to the field lines it must be acted upon by the Lorentz force
Calculation 2
- If we equate the two forces we get
- We can then rearrange to get the radius of the circle
Particle Accelerators
A cyclotron is a method of accelerating particles.
Cyclotrons
- A cyclotron is made up of two semi-circular plates separated by a gap with a potential difference across it.
- A magnetic field is applied so that it is perpendicular to the semi-circles.
- Charged particles follow a circular path parallel to the plates due to the magnetic field.
Accelerating
- A positive particle reaches the gap every half rotation.
- The voltage drop accelerates the particle towards the negative terminal across the gap.
- The voltage across the gap is varied on every half rotation so that the particle speed is always increased.
Radius
- The radius of the circular motion is given by
- As the velocity of the particle increases, the radius of its circular motion increases.
- The particle spirals out of the machine at a very high speed.
Test yourself on Moving Charges in a Magnetic Field
In what direction does the Lorentz force act?
Particles in a magnetic field undergo what type of motion?
What is a cyclotron used for?
Which of these is true about cyclotrons?
What is put across the gap in the plates of a cyclotron?