Are there any other notable assumptions I've missed in my lab write-up?

Question

Let's say I have to write a lab report that includes notable assumptions made that are pertinent, significant and relevant to my experiment. The purpose of my experiment is to determine the permittivity of free space experimentally to within the same order of magnitude as the generally accepted value.

My experiment is a Coulomb balance where you set up a balance of two flat capacitor plates (~12cm x 12cm) and afterwards introduce a known weight (50mg). A mirror is attached to the top (freely swinging) arm of the balance which then reflects a laser onto a target, showing the deviation that the weight caused. I then wire the two plates up to an electrical potential that I can control and remove the weight. I increase the voltage until I see the same deviation of the laser, the point being that I can then equate the known gravitational attractive force to the electrical one and calculate out a value for the permittivity of free space.

So far for my assumptions I have :

a) The capacitor plates' thicknesses are irrelevant (or at least thin enough to be negligible).

b) The permittivity of free space resembles that of air closely enough.

c) All equipment and apparatus used have no significant internal resistance, conduct electricity fairly perfectly and have no error in labelling or value reporting.

d) All equipment and apparatus used have no significant and unwanted inherent magnetic residue.

There is a separate part where I account for/write about sources of error. I'm not looking for additional sources of error - correct me if I'm wrong, but a source of error is not the same as an assumption. I can't think of anything else that I should include in this list but I'm fairly certain there must be more assumptions that I haven't thought of. Any thoughts ?

Answer 1

As you are only looking for order-of-magnitude accuracy, I do not think it is appropriate to mention assumptions which are unlikely to have a significant effect on the result. There is no point identifying assumptions just for the sake of having an impressive number of them. Quality (significance) is more valuable than quantity here.

a) Thickness of plates. I don't see what effect this might have, so I would say it is not worth mentioning. The usual assumption that $L \gg d$ is worth mentioning. Whether or not this assumption is justified depends on the accuracy of your measurement. For order of magnitude accuracy your values justify this assumption.

b) Yes. Ideally you would perform the experiment in vacuum, but that would involve too much effort. You might compare standard values for permittivity of air and vacuum to justify this assumption.

c) Yes. This relates to measurement of $V$ between the plates.

d) I don't see the significance of this, particularly because you are using magnetic damping. If you include this I think you need to explain how you think residual magnetism might cause a significant (order of magnitude) error. Magnetic forces might have an influence when there are currents or moving charges, but not with static electricity.

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I presume the key equation you used is
$F=\frac{\epsilon L^2V^2}{2d^2}$.
The squared quantities potentially introduce the largest errors, so you need to concentrate on those, especially those which have the largest % error. I think measurement of $d$ introduced the biggest source of error.

You seem to have done a careful experiment. You performed several runs. I expected that you would vary $m$ and $V$ to check that $m \propto V^2$ as your equation predicts.

The only other source of error I can think of is possible bending of the pivot arm. This would cause the plates to mis-align from parallel. But I expect the arm is quite stiff and $m=50g$ too small to cause a significant effect, so this is probably not worth mentioning.