# Mass of an electron lab discussion?

1. May 17, 2012

### Wh1994

1. The problem statement, all variables and given/known data
Hi, I did a lab for a high school physics class where we measured the mass of an electron using a solenoid and our working equation was this:

m = qB2R2/2V

I was able to do the lab and get good results, but I have discussion questions I don't know how to answer. I can't figure it out. Here are the questions:

Would it be possible to use the earth's magnetic field to deflect the beam? How large a tube would you need? Assuming the earth had no magnetic field, would it be practical to determine the mass of an electron by accelerating it horizontally through a known potential difference and subsequently observing its deflection in the earth's gravitational field?

2. Relevant equations
e/m ratio?

3. The attempt at a solution

2. May 17, 2012

### turin

Your instructor wants you to try to understand your formula, which is based on a few ostensibly disparate concepts that have been combined for you into a neat little package. (Physicists get such a kick out of deriving equations like the one you used in your lab to calculate the mass from the measured parameters). I will lay out the basic physics principles that come into play, first conceptually, and I hope that this will give you a good direction.

Newton's Second Law: force acting on the electron causes it to accelerate, and this acceleration is impeded by the mass of the electron. What is the nature of this acceleration (i.e. speeding up, slowing down, changing direction, or a combination)? Think about the path of the electron: was is straight or curved. Did you measure a rate of CHANGE in speed? What is the origin of the force? The mass of the electron is probably the m in your formula.

centripetal motion: this motion is characterized by a changing direction, and therefore an acceleration, and therefore requires a force. The radius of the circular path here is probably the R in your formula. The speed of the electron is probably the V in your formula.

magnetic force: this is imposed on a charged particle that moves through a magnetic field. The field strength is probably the B in your formula, and the charge is probably the q in your formula.

3. May 17, 2012

### truesearch

I think the equation you have quoted relates to a well known demonstration. The electrons are accelerated through a voltage V then pass into a region between 2 large coils (your solenoid) These coils are known as Helmholtz coils and produce a uniform magnetic field, B.
This field causes the electrons to travel in a circular path of radius,r, because the force due to the magnetic field is the centripetal force for the electrons.
The magnetic field is calculated from the dimensions of the helmholtz coils and the current flowing through them. If you compare the field you calculated with the Earth's magnetic field it should give you some idea of the radius of the path followed by the electrons in the earth's field and hence the size of the container.
Do you see how the equation comes about by considering the KE gained by the electrons in the accelerating voltage and the force due to the magnetic field being the centripetal force?