# Help calculating the mass of an electron

1. Jan 9, 2010

### Cookyt

I'm setting up an experiment where I have a circular cathode releasing electrons to an outer circular anode. The tube is inside an induction coil, and when turned on, the coil provides a magnetic force on the electrons causing them to go into uniform circular motion.

The purpose of my experiment is to measure the radius of the electron beam, and use it to calculate the mass of an electron; however, the results range anywhere from a 8% to a 2000% difference. I charted a graph of radius vs magnetic field using the equation:

r = (1/B) * $$\sqrt{}(2Vm/q)$$

B is the magnetic field
V is the potential difference between my cathode and anode
m is the mass of an electron
q is the charge of an electron.

this was derived from the two equations:

qveB = m(ve2/r)
qV = (1/2)mve2

where ve is the velocity of an electron

my r values are incredibly small (fractions of a cm) when I use this equation, and I'm all out of ideas. Can anyone see the flaws in my reasoning?

2. Jan 9, 2010

Staff Emeritus
If the radius is too small, it means the magnetic field is too big.

3. Jan 9, 2010

### Bob S

See
http://www.pas.rochester.edu/~pavone/particle-www/teachers/demonstrations/e over m.htm
It is probably best if you start with MKS units for everything: volts, Tesla, meters, and finally Coulombs per kilogram (yes) for e/m. Remember that 1 mol of electrons have a mass of about 1/1837 grams.
Bob S

[added] Here is a fully relativistic equation I use for "B-rho"

Bρ = (βγ/c) m0c2 Tesla meters

where m0c2 is 511,000 electron volts.

Last edited: Jan 9, 2010
4. Jan 9, 2010

### Stonebridge

I may be misunderstanding the experimental setup here, but are the electrons moving in a circular path between the cathode and the anode? Orbiting the cathode, as it were?
If that is the case, then they are in the electric field produced by the cathode/anode pd and as such experience a force towards the anode due to this field. This must also be taken into account when you consider the centripetal force on the electrons. In other words, the magnetic force. qvB, is not the only force acting to produce circular motion.
Secondly, the equation for kinetic energy of the electrons (=qV) assumes the electrons have fallen through the complete pd (V) between the cathode and anode. This is not the case if they are moving in a circle of radius r where r is less than the distance to the anode. They have only fallen through a fraction of this voltage, depending on the value of r.
As I say, I may be visualising this incorrectly, but it doesn't seem to be the same experimental setup as BobS has kindly linked to. In that setup the equations would be correct.

5. Jan 9, 2010

### Bob S

In one laboratory electron e/m measurement, the electrons are accelerated to the anode in a vacuum tube, and a few electrons pass through a hole in the center of the anode into a field-free region where the electrons drift at constant velocity in a transverse magnetic field. See attachment.
Bob S
Picture from http://phoenix.phys.clemson.edu/labs/cupol/eoverm/

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6. Jan 10, 2010

### Stonebridge

I agree, Bob, that this is the standard way of doing the e/m calculation. However, the poster's description in the 1st post got me wondering if this was some other method. (One I'm not aware of). If so, as well as explaining my incredulity, it would also explain why, using the standard equations, the results are causing a problem.

7. Jan 10, 2010

### Bob S

The magnetron oscillator vacuum tube (like in a microwave oven) frequency is

ω = eB/mc radians per second.

Se Eqn 2.4 in http://hussle.harvard.edu/~gabrielse/gabrielse/papers/1992/1992_tan/chapter_2.pdf

So measuring the magnetron tube frequency as a function of the applied magnetic field is another way of measuring e/m.

Bob S

Last edited by a moderator: Apr 24, 2017