# Error analysis E/M experiment -- help please

Kamal98
So I am doing the charge to mass experiment and determining the relationship between:
1. accelerating voltage and radius formed by the electron beam
2. magnetic field strength and radius formed by electron beam

Theoretically I should obtain an equation of the form:
r = (1/B) *sqrt(2mV/e)
where B is the magnetic field strength, V is the accelerating voltage and e and m the charge and mass of an electron. However after doing the experiment and plotting the graphs I get a y-intercept in the graph equation which should not be there.

I am trying to explain the reason for the intercepts. The graphs are in the link below:

Now, firstly the error on the value for r (the radius) is enough to explain the intercepts. Drawing graphs at the extreme ends of the error bars shows that the y-intercepts varies from a positive value to a negative value meaning that the intercept becomes zero at some point between the error bars. However I was wondering if this could also be explained through the earth's magnetic field strength. In the experiment, the apparatus has to be aligned in the earth's north-south direction, a dip needle is then used to determine the dip angle and the apparatus is elevated to the angle to cancel out the effects of the earth's magnetic field. This is important as it affects the trajectory of the electrons. However, I did not do this in my experiment. So it is a source of error. But I do not know how to determine the impact of this and whether it will be larger or smaller than the error already present on r.

I can in a way justify that taking this into account would have made the graphs more 'ideal' correcting the intercepts to near zero. But its not concrete.
Another thing:
The earth's magnetic field strength is of the order 10^-5T and the magnetic field strength in my experiment was made through helmholtz coils and the field strength varied from an order of 10^-4T to 10^-3T. Is the order of the earth's field big enough to impact the field created by the coils?

Can anyone enlighten me on this? I know its not a straightforward answer.

scottdave
Homework Helper
How much y-intercept are you getting? Looking at your screenshots, and trying to extend a straight line, it looks pretty close to hitting the "origin", to me. Note that your "axis" starts at 5 Volts0.5 rather than 0. So you need to extend all the way down to zero V0.5.

Kamal98
How much y-intercept are you getting? Looking at your screenshots, and trying to extend a straight line, it looks pretty close to hitting the "origin", to me. Note that your "axis" starts at 5 Volts0.5 rather than 0. So you need to extend all the way down to zero V0.5.
Yes, its -0.0016 for the first graph and +0.0029 for the second. So you are saying its pretty much negligible?

scottdave
Homework Helper
To me, those numbers seem close enough to zero. If you could perform the experiment more than one time, that would tell you, for sure. Or compare with other students to see if the variations seem consistent with the experiment.

scottdave
Homework Helper
So the Earth's magnetic field strength is from 1% to 10% of your applied field, but in which direction relative to the motion or the applied field?

Kamal98
I just had a chat with my teacher on this. I don't know the direction of the earth's field relative to my field. But the field is from 1% to 10% as Dave said. So I'll add just the earth's field to my field to get the largest possible value for the net field and then subtract to get smallest possible value for the net field. So my field will have an uncertainty. Then I'll go from there and compare that to the error on the radius r.

scottdave