In an experiment I measured the surface charge density of a thin, charged, metal plate. I found, as expected, $\sigma$ to be constant over the surface, however at the edge of the plate it became abnormally large. I repeated the measurement a couple of times but with the same result. I didn't find anything online, and with my current knowledge I would say $\sigma$ is constant throughout the plate and that something just went wrong with that last measurement. Am I correct in my thinking? See below for the actual data. It may also be important that there was a grounded metal plate opposite to the charged one, however it was quite far away (12cm)
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Urb
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@josephh I don't think my university will allow me to redo the experiment. How would you think it impacts the result? – J.S.A. Frugte Mar 13 '21 at 04:14
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Maybe this will be helpful: https://physics.stackexchange.com/q/95584/291127 – Cluse Mar 13 '21 at 04:18
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4It is important to describe how you measured the "surface charge density". As far as I know, there is no device to make this measurement. In your plot your y-axis is labeled with "voltage". What did you measure? What device did you use? – verdelite Mar 13 '21 at 04:19
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Your observation is consistent with the theory. The surface charge density, denoted by σ, is not necessarily constant over the surface of a conductor. It can vary depending on the geometry of the conductor.
In fact, the surface charge density is inversely proportional to the radius of curvature on the conductor. This means that on a flat surface, where the radius of curvature is infinite, the surface charge density would be relatively low. However, at the edges of the plate, where the radius of curvature is small, the surface charge density would be expected to be higher.
This phenomenon is due to the fact that charges repel each other. On a flat surface, the charges spread out evenly. But at the edges, they can't get any farther apart, so they accumulate, leading to a higher surface charge density.
So, your measurements showing a higher surface charge density at the edges of the plate are not an error, but rather an interesting physical phenomenon! I hope this helps clarify your understanding.
Vish
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Worth noting that this statement "the surface charge density is inversely proportional to the radius" applies to situations where ground is infinitely far away in all directions (I assume? right?). Here ground is "a grounded metal plate 12cm away." Since the plate measured here is 20cm diameter, this approximation is not valid. In the center it's more like parallel plates, which have density $\sigma=\epsilon V/d$ (distance d apart, voltage V) - a nonzero charge density despite having infinite local radius of curvature. It remains true thought that curved spots will have higher charge density. – AXensen Feb 21 '24 at 01:12
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I don't know what you are experimental methods were, still the measurements comply with what one would expect from the theory.
Surface charge density is inversely proportional to the radius of curvature on the conductor.
Assuming in the conducting plate has a near infinite radius of curvature where it is flat and very small radius of curvature at the edges, assuming sharp turns; it would completely make sense to expect very high surface charge density at the edges then from the flat surface.
SteelCubes
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curvature of the surface affects charge density if the surface is in equipotential. walter lewins lectures explain this https://youtu.be/ww0XJUqFHXU
jensen paull
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