Electrostatic induction with planes -

[joker_900]

Homework Statement

Two large plane parallel 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 a disstance b (<D) from one of them. What proportion of the charge +q is induced on each of the two plates?

Homework Equations

The Attempt at a Solution

I've been told the way to do this is to replace the point charge with a plane conducting sheet inserted between the plates a distance b from one of them, with a charge +q on it, and find the charges induced on the plates. However I can't work out how to do this. I've tried using Gauss' Law to show that the flux out of this new plate in each perpendicular direction is q/e0 and so the resultant fiels in each perpendicular direction is q/Ae0 but to no avail. Please help!

 

[anathema]

Thank you for your question. It seems like you are on the right track with using Gauss' Law to solve this problem. However, instead of trying to find the flux out of the new conducting sheet, try to think about the electric field lines that will be present in the space between the two plates.

When a point charge is placed in an electric field, it will experience a force in the direction of the electric field lines. In this case, the point charge +q will experience a force towards the conducting sheet. This means that there must be an electric field present in the space between the two plates, pointing towards the sheet.

Now, using Gauss' Law, you can determine the electric field between the plates due to the presence of the conducting sheet. Once you know the electric field, you can use the formula for capacitance to determine the charge induced on each of the plates. Remember that the electric field between two parallel plates is uniform, so you can use the formula E = V/d to find the electric field between the plates.

I hope this helps. Good luck with your problem!

 

[Moetasim]

The proportion of charge induced on each plate can be determined by considering the electrostatic induction between the two plates. When a charged particle is placed in the electric field between two conducting plates, the electric field causes a redistribution of charges on the plates, resulting in an induced electric field. This induced electric field will cause a force on the charged particle, pushing it towards one of the plates.

In this case, the point charge +q is placed at a distance b from one of the plates. This will create an induced electric field, which in turn will induce a charge on the plates. The magnitude of the induced charge on each plate can be determined by using the formula Q = CV, where Q is the charge, C is the capacitance, and V is the potential difference between the plates.

In this case, the capacitance can be calculated by using the formula C = εA/d, where ε is the permittivity of vacuum, A is the area of the plates, and d is the distance between the plates. The potential difference can be calculated by using the formula V = Ed, where E is the electric field created by the point charge +q.

Using these formulas, we can calculate the induced charge on each plate. The proportion of charge induced on each plate can then be determined by taking the ratio of the induced charge to the total charge +q.

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