Calculating the capacitance problem

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SUMMARY

The discussion centers on calculating the ratio of capacitance to area (C/A) for an uncharged parallel-plate capacitor connected to a battery. The problem states that when the depth (d) from which electrons originate is one picometre, the potential difference (V) is 20V, with a gradient of 5x10-14. The user attempts to derive the ratio using the equations q=ε₀EA and q=CV, ultimately finding that C/A=ε₀/D, but struggles to interpret the meaning of the gradient and its units.

PREREQUISITES
  • Understanding of capacitor fundamentals, specifically parallel-plate capacitors.
  • Familiarity with the equations governing capacitance, including q=ε₀EA and q=CV.
  • Knowledge of electrical potential difference and its relationship to charge and capacitance.
  • Basic grasp of gradients in mathematical contexts, particularly in physics.
NEXT STEPS
  • Research the physical significance of the gradient in capacitor charge distribution.
  • Explore the relationship between capacitance, area, and distance in parallel-plate capacitors.
  • Study the implications of ε₀ (the permittivity of free space) in capacitor calculations.
  • Investigate the units of measurement for potential difference and their relevance in electrical equations.
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Students studying electrical engineering, physics enthusiasts, and anyone seeking to understand capacitor behavior in circuits.

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Homework Statement


If an uncharged parallel-plate capacitor (capacitance C) is connected to a battery, one plate becomes negatively charged as electrons move to the plate face (area A). The depth d from which the electrons come in the plate in a particular capacitor is plotted against a range of values for the potential difference V of the battery. When d is one picometre, the potential difference is 20V. The gradient is equal to 5x10-14. What is the ratio C/A.

Homework Equations



q=ε₀EA
q=CV

The Attempt at a Solution



I combined the above two equations to get the expressions C/A=ε₀/D
However that doesn't provide me with a numerical solution for the ratio C/A.

Can anyone please help?
 
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I don't understand what is meant by "the depth ... from which the electrons come in the plate".

Also, what is this "gradient equal to 5x10-14" mean? And what are the units?
 

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