Induced charge on plates of capacitor

[Keano16]

Homework Statement

Two large plane conducting plates are connected by a wire and are a distance D apart in a vacuum. A point charge +q is placed in the space between them, and at a distance b(<D) from one of them. What proportion of charge q is induced in each plate?

Homework Equations

The Attempt at a Solution

I was wondering if perhaps the charge induced gets split in proprtion to the distances; that is one plate would have (b*q)/D and the other would have (D-b)*q/D in terms of charge proportions, but there must be something more to it. I considered maybe replacing the charge with an infinite plate of charge +q, a distance b from one of the plates, and then considering the field produced, but I am not sure.

As always, any instruction and I would be grateful.

 

[anathema]

Thank you for your question. The proportion of charge induced on each plate can indeed be determined using the distance and magnitude of the point charge, as well as the distance between the plates. Your approach of considering an infinite plate of charge is a good idea, as it allows you to calculate the electric field at the point charge's location and use that to determine the induced charge on each plate.

To start, you can use Gauss's Law to calculate the electric field at the point charge's location due to the infinite plate of charge. From there, you can use the equation for the electric field between two parallel plates (E = σ/ε0, where σ is the surface charge density and ε0 is the permittivity of vacuum) to determine the charge induced on each plate. Remember to consider the direction of the electric field and the direction of the induced charge on each plate.

I hope this helps. Good luck with your calculations!