Electrostatic repulsion formula for plates

[joshste86]

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

 

[kanato]

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 $$U = \frac12 CV^2$$ and $$C = \epsilon A/d$$. (Take care about whether you are keeping voltage or charge constant.)

 

[astrokreng]

Hello,

That is correct, Coulomb's Law only applies to point charges. When dealing with plates, we use the formula for electrostatic repulsion between parallel plates. This formula is known as the "plate capacitor formula" and it is given by F = ε0A(V/d)^2, where F is the force of repulsion, ε0 is the permittivity of free space, A is the area of the plates, V is the voltage between the plates, and d is the distance between the plates. This formula assumes that the plates are large in comparison to their separation distance.

To determine the voltage required to maintain a charge within the plates, we use the formula Q = CV, where Q is the charge on the plates, C is the capacitance of the plates, and V is the voltage between the plates. The capacitance, in turn, is given by C = ε0A/d, where ε0 is the permittivity of free space, A is the area of the plates, and d is the distance between the plates. Therefore, the formula for the voltage required to maintain a charge within the plates is V = Qd/ε0A.

I hope this helps! Let me know if you have any further questions.