Consider a capacitor with circular plates radius R and charges Q on one plate an
ID: 1309317 • Letter: C
Question
Consider a capacitor with circular plates radius R and charges Q on one plate and -Q on the other plate. Use Gauss' Law to show that E = sigma / upsilon 0 (-k) in the space between the plates if the plates are separated by a distance d R on the z-axis and the top plate is positive. Neglect fringing Write out the complete stress tensor for the region between the plates as a 3x3 matrix. Neglecting any fringing of the fields construct an appropriate closed surface around the top plate and integrate n dA over the surface to get the force between the plates. Show your work. Which way does the force between the plates point?Explanation / Answer
A)
The electric field due to the positive plate is
?/?0
And the magnitude of the electric field due to the negative plate is the same. These fields will add in between the capacitor giving a net field of:
2?/?0
If we try getting the resultant field using Gauss's Law, enclosing the plate in a Gaussian surface as shown, there is flux only through the face parallel to the positive plate and outside it (since the other face is in the conductor and the electric field skims all other faces).
?=?E? ?dA?=EA
where E is the electric field between the capacitor plates. From Gauss's Law this is equal to the charge Q on the plates divided by ?0
b) for the stress tensor , you can find exactly what u need in this pdf's 3rd page
http://www.hep.princeton.edu/~mcdonald/examples/cap_stress.pdf
c) the above link has the solution for this part too !!
Q/?0?E=Q/A?0=?/?0
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