Two positively charged plates : interaction force

AI Thread Summary
The discussion revolves around the interaction force between two positively charged plates, each with charge Q and area A. A paradox arises as the calculated force suggests it should be zero due to the absence of an electric field between the plates, despite the expected attraction based on Coulomb's law. The energy stored in the electric field is also debated, as it appears to contradict the force calculation, particularly when considering fringe effects. The conversation highlights the importance of using the infinite sheet approximation correctly, as it fails when the separation between plates is not negligible compared to their dimensions. Ultimately, the need to account for fringe fields and the limitations of energy density calculations are emphasized.
Perpendicular
Messages
49
Reaction score
0
Hello,

I am facing a paradox, well it seems like one, resolving the interaction force between two equally charged plates each bearing a positive charge. Let us assume this as Q, and plates having area A.

On one hand , we can claim the force = Q^2/2Ae0 where e0 is the vacuum permittivity, as each plate bears a charge Q and generates a field Q/2Ae0 at points not too far off from itself or close to the edges.

But, if we look at the energy stored, I am getting a very different result. There is no field in the region between the two plates so the energy field density 1/2e0(E^2) is zero. Outside the plates, the electric field will remain ~ Q/2Ae0 from each plate, totalling Q/Ae0 at first and then begin trailing off as we go farther and farther. Eventually it will trail off completely. So if we move a plate, this trailing off merely starts at a different point and the net energy stored outside each plate is conserved. Hence energy is a constant therefore F = -dE/dr = zero. I can't accept this logically but neglecting the fringe field, this seems to imply some sort of internal screening of charges.
 
Physics news on Phys.org
There is no field in the region between the two plates...
How do you figure that?
 
Because at points not too far off to the edge, or corners, the field due to each plate can be approximated as charge density/2e0. They act in opposite directions.

I now realize though, this probably implies the fringe field is non-negligible in this case..
 
Oh I see, you wanted to make an approximation for the case that the dimensions of the sheets are very large compared with their separation - the infinite sheet approximation?

To use Gausses Law and F=qE ideas, each distribution of charge moves in the potential due to the other charges.

So each plate feels the force due to the field due to the other plate alone.
You appear to have been combining the fields in your arguments.

When in doubt though: return to Coulomb's law.
 
I know that each plate feels the field due to the other plate alone. I just want to derive that via energy stored in the electric field, and this seems to be impossible without the fringe field which is in turn very hard to numerically figure out. Ignoring it, I get F = zero which is absurd.
 
Well yes - the shortcut you tried (via energy density between the plates) (a) combines the fields, and (b) relies on the infinite sheet approximation ... which is not valid when the separation is comparable to or bigger than the dimensions of the sheets - which is what happens for the stored energy calculation since the sheets start at infinite separation.
 
Thread 'Griffith, Electrodynamics, 4th Edition, Example 4.8. (Second part)'
I am reading the Griffith, Electrodynamics book, 4th edition, Example 4.8. I want to understand some issues more correctly. It's a little bit difficult to understand now. > Example 4.8. Suppose the entire region below the plane ##z=0## in Fig. 4.28 is filled with uniform linear dielectric material of susceptibility ##\chi_e##. Calculate the force on a point charge ##q## situated a distance ##d## above the origin. In the page 196, in the first paragraph, the author argues as follows ...
Thread 'Inducing EMF Through a Coil: Understanding Flux'
Thank you for reading my post. I can understand why a change in magnetic flux through a conducting surface would induce an emf, but how does this work when inducing an emf through a coil? How does the flux through the empty space between the wires have an effect on the electrons in the wire itself? In the image below is a coil with a magnetic field going through the space between the wires but not necessarily through the wires themselves. Thank you.
Back
Top