Electrons in a uniform magnetic field. (1959)

with this apparatus you will be able to see what happens to electrons when they are acted on by electrical forces and magnetic forces that we can produce and measure one of the things that we'll be able to determine from our observations is the mass of an electron this tube contains a little hydrogen and over here there's an electron gun aimed upward the source of electrons is a heated cathode at the bottom of the gun the electrons are accelerated upward by a potential difference applied between between the cathode and the cone-shaped anode above it the accelerating potential we read on this meter now once we have a moving stream of electrons we have a second way of controlling their motion namely by a magnetic field we know that a charge moving across a magnetic field has a deflecting force on it we use these coils to produce our magnetic field a current flowing around a circular coil like this produces a magnetic field at the center that has a direction perpendicular to the face of the coil and a magnitude proportional to the current flowing this apparatus has two coils arranged in such a way that there is a very uniform field between them so that wherever an electron is found within the tube the effect of the field will be the same coils arranged in this way these are one coil radius apart are known as Helm Holtz coils you can see that the electrons are going to be moving upward in this direction the field is horizontal in this direction or perpendicular to the motion of the electrons to measure the field strength we read the current in the coils on this meter I've made a calibration showing the magnitude of the field for each value of the current as you might expect it's a straight line in other words the field is proportional to the current now let's turn on the tube we'll start with no magnetic field that is with no current in the coils as I turn up the gun voltage which you can read on the top meter we see the beam of moving electrons it's visible or at least visible in the dark because the electrons make the gas in the tube glow along the path of the stream now notice that since we know the voltage applied to the gun we know the kinetic energy of the electrons as they leave the gun the energy of an electron as it leaves the gun is equal to the energy per Elementary charge times the charge we have 100 volts on the electron gun and each volt is worth this many jewles per Elementary charge and now an electron has one Elementary charge so our Q is one and this is the energy energy of one electron as it leaves the gun now let's turn on the magnetic field which will change the direction of the electrons but of course won't change this kinetic energy this time watch the ammeter at the bottom as we increase the field we increase the deflecting force on the beam remember the magnetic field is perpendicular to the path of the electrons everywhere on the path thus the magnetic force is the centripetal force acting on the electrons this force that keeps the electrons moving in a circular path of radius R is equal to the field times the charge times the velocity of the moving electrons since V occurs on both sides of this equation we can write this more simply in terms of momentum and we have quantities now that we can measure we can measure B the field by reading the current and using our calibration curve the current in the coils is 79 amp that gives for the field 97 * 10- 22 so we have this for the field and Q is still one and now we have to measure R now of course we can't put a ruler inside the tube and measure R directly so we have to use some kind of trick there are a number of ways we could do this but what I've done is this I've taken a picture of the circle formed by the Electron Beam then I've removed the tube and I've taken another picture of a scale put in exactly the same plane occupied by the beam here are the pictures I've cut this along the scale and now I can use it to find the diameter of the Electron Beam the diameter is 11 cm and R is half of this 5 12 CM or 055 M so here we have the momentum of an electron traveling in the particular Circle that we've been watching now it's clear that from these two equations we can determine both the mass and the velocity and when we do this for the particular values we have here we get the mass of an electron is equal to 89 * 10-30 kg incidentally the Velocity in this case is about 6 * 10 6 m/ second now I have the results of some other measurements that we've made with different values of v and B here you can see that although the accelerating potential varies quite a bit and the field varies giving different values for the radius of the circle and for the velocity of the electrons still the value that we get for M turns out to be always just about 10 - 30 in other words no matter how we do this experiment we always get about the same value for the mass of an electron we can also check very easily how the radius of the Electron Beam depends on the voltage and current you can see that by increasing the voltage and thus the energy of the electrons we make the circle larger increasing the field F makes it smaller in fact if you want to do a little algebra you can find out from these two equations exactly how R should vary with v and B finally let's do one more thing so far we've been shooting the electrons straight up perpendicular to the field what would happen if we were to shoot them at an angle so that there would be a component of their velocity parallel to the field as well as one perpendicular I'll rotate the tube like this so that the direction in which the gun is aimed will make different angles with the direction of the field the vertical component of the electron velocity will still be affected by the magnetic field but not the horizontal component here the gun's direction is at right angles to the field as I change the angle the electrons continue to circle around the direction of the magnetic field but also move along the direction of the field until they hit the glass I think you could predict the shape of this Helix all you need to know is the field the gun voltage and the angle of the gun