Electrostatic repulsion formula for plates

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SUMMARY

The discussion centers on the electrostatic repulsion between charged plates, specifically parallel plate capacitors. The force between two plates can be calculated by differentiating the energy stored in the capacitor, represented by the equation U = ½ CV², where C is the capacitance. The capacitance for parallel plates is given by C = εA/d, where ε is the permittivity, A is the area of the plates, and d is the distance between them. Additionally, the relationship between charge (Q), capacitance (C), and voltage (V) is defined by the equation Q = CV.

PREREQUISITES
  • Understanding of Coulomb's Law and its application to charge distributions
  • Familiarity with the concept of capacitance in parallel plate capacitors
  • Knowledge of electrostatic energy calculations
  • Basic algebra for manipulating equations involving voltage, charge, and capacitance
NEXT STEPS
  • Research the derivation of the capacitance formula for parallel plate capacitors
  • Learn about energy storage in capacitors and its implications for circuit design
  • Explore the integration of charge density for complex charge distributions
  • Study the effects of varying distance between plates on electrostatic force
USEFUL FOR

Physics students, electrical engineers, and anyone interested in understanding electrostatics and capacitor behavior in electrical circuits.

joshste86
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Hey all

I read somewhere online that Coulomb's Law only applies to spheres and point charges, and was wondering what formula is used to calculate the force between 2 plates whilst charged the same polarity

Also, what is the formula to determine how much voltage is required to maintain a charge within the plates?

cheers
 
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Coulomb's law applies to any charge distribution, but if it's complex you have to integrate over the charge density to get the correct result. This can lead to more or less complex expressions depending on the charge distribution.

For a parallel plate capacitor, the equation is Q = CV where C is the capacitance, Q is the charge and V is the voltage.

The easy way to calculate the force between to parallel plates is to calculate the energy, and then differentiate with respect to the distance between them. You can do this using [tex]U = \frac12 CV^2[/tex] and [tex]C = \epsilon A/d[/tex]. (Take care about whether you are keeping voltage or charge constant.)
 
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