How Do You Calculate the Diameter of Plates in a Parallel Plate Capacitor?

AI Thread Summary
To calculate the diameter of plates in a parallel plate capacitor, start by determining the charge on the plates using the formula for charge, which is the number of electrons multiplied by the elementary charge, resulting in 6.24x10^-10 C. Next, apply the relationship between electric field strength (E) and charge density (σ) for a uniformly charged plate, where E = σ / (2ε₀), with ε₀ being the permittivity of free space. Since the problem specifies that the distance between the plates is small compared to their diameter, you can use Gauss' law to derive the necessary equations. Ultimately, solving for the diameter involves rearranging these equations to express diameter in terms of the known charge and electric field strength. The final result will provide the diameter of the capacitor plates.
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Homework Statement



A parallel plate capacitor is made of two circular disks. The distance between the disks is very small compared to their diameter. Initially, the disks are electrically neutral. After transferring 3.9x10^9 electrons from one disk to the other, the electric field strength in the space between the plates is 1.0x10^5 N/C. What is the diameter of the plates?

e = 1.6x10^-19C


Homework Equations





The Attempt at a Solution



I was able to calculate the charge on the plates by multiplying the number of electrons by their fundamental unit charge:

3.9x10^9 * 1.6^10-19C = 6.24x10^-10C

However I'm really lost as to what to do next. Any guidance would be much appreciated.
 
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Can you find or derive an equation that gives the electric field of a uniformly charged plate or plane? An equation relating to a capacitor might help.

If you can't find an existing equation, Gauss' law can help you derive it (given that the problem states "distance between the disks is very small compared to their diameter").
 
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