About this experiment
An electric field pushes a charge along the field lines, so a particle fired between charged plates bends into a parabola, just like a ball thrown sideways. A magnetic field does something stranger: it pushes at right angles to the motion, so the particle never speeds up or slows down but curves round in a circle. Fire electrons, protons and alpha particles into electric and magnetic fields, measure the radius of the circle, and balance the two forces to build a velocity selector.
Learning goals
- Describe the parabolic path of a charged particle in a uniform electric field
- Explain why a magnetic field changes the direction but not the speed of a moving charge
- Use r = mv / qB and T = 2πm / qB for circular motion in a magnetic field
- Explain how crossed electric and magnetic fields select particles of one speed, v = E / B
- Compare the paths of particles with different charge and mass
How to use it
- 1Choose Electric field only and fire an electron. Which way does it bend? Switch to a proton. Why does it bend the other way?
- 2Choose Magnetic field only. Measure the diameter of the circle with the 10 cm scale and compare with the radius readout.
- 3Double the magnetic field. What happens to the radius? What happens to the period?
- 4Increase the accelerating voltage four times. By how much does the radius change? Explain using r = mv / qB.
- 5Fire a proton and an alpha particle with the same voltage and field. Which circle is bigger?
- 6Choose Velocity selector so the particle goes straight. Now change the voltage only. Does it still go straight?
The model
Assumptions
- The fields are uniform inside the 40 cm by 30 cm box and zero outside it. Gravity is far too weak to matter and is ignored.
- Speeds are much smaller than the speed of light (at 5000 V an electron reaches about 14 % of it), so classical mechanics is used.
- The path is integrated with the Boris method, which keeps the speed exactly constant in a pure magnetic field. A moving charge also radiates, which is ignored.
- Each particle enters at the middle of the left edge, moving to the right, after being accelerated from rest by the chosen voltage.
Try this in class
- Q1An electron accelerated through 2000 V enters a 1.5 mT magnetic field at right angles. Find its speed and the radius of its path.
- Q2Why does a magnetic field do no work on a moving charge?
- Q3Show that the period of circular motion does not depend on the speed. Why is this useful in a cyclotron?
- Q4In a velocity selector E = 20 kV/m and B = 0.05 T. What speed passes straight through?
- Q5A mass spectrometer bends ions of the same speed and charge in a magnetic field. How does this separate isotopes?
Frequently asked questions
What do the dots and crosses mean?
They show a magnetic field at right angles to the screen. Dots are arrow tips coming towards you, so the field points out of the screen. Crosses are the tail feathers of arrows going away, so the field points into the screen.
Which way does the magnetic force push?
Use the right-hand rule for v × B, then reverse it for a negative charge such as an electron. In the simulation the purple arrow always points towards the centre of the circle.
Why is a proton circle so much bigger than an electron circle?
A proton is about 1836 times heavier. After the same accelerating voltage it moves more slowly, but its momentum mv is about 43 times bigger, so the radius r = mv / qB is about 43 times bigger in the same field.