Point charge and a plane question

[joker_900]

OK I'm really not understanding any of this, please help, and any tips on how to go about problems like this in general would be much appreciated.

Homework Statement

A point charge Q is situated a distance d from an infinite conducting plate connected to ground. Show that the total charge on the conductor is -Q.

Homework Equations

I'm not sure but I think the Gauss equations?

The Attempt at a Solution

I've found the electric field at any point on the plane to be

[kQ/(x^2 + y^2 + d^2)^(3/2)] (-x, -y, d)

But like I said, I don't really know what I'm doing!

 

[Mindscrape]

Do you know the method of images? I suppose that regardless of whether or not you know, you ought to learn it to do the problem. This is a really standard image problem, and I think that once you look it up that you will not have any problems.

Edit:
I don't know how far you plan on going in physics, if for example you will do EM with vector calculus, but Griffiths definitely has the best EM book out there, and now that I look this exact problem is an example he goes over.

 

[Moetasim]

Hi there,

I understand that this topic can be confusing, but I will try my best to explain it to you. First, let's start with the concept of a point charge. A point charge is an object that has an electrical charge concentrated at a single point. It can be either positive or negative, denoted by Q. The electric field around a point charge is given by the equation:

E = kQ/r^2

Where k is the Coulomb's constant and r is the distance from the point charge.

Now, let's move on to the infinite conducting plate. A conducting plate is a material that allows charges to move freely on its surface. In this case, the plate is connected to ground, which means that it has a net charge of zero.

Now, let's consider the point charge Q, which is situated a distance d from the conducting plate. The electric field due to Q will induce a charge on the surface of the plate. This induced charge will create an electric field of its own, which will cancel out the electric field due to Q at the surface of the plate. This means that the net electric field at the surface of the plate is zero.

Using Gauss's Law, we can show that the total charge on the conductor is -Q. Gauss's Law states that the flux of the electric field through a closed surface is equal to the total charge enclosed by that surface divided by the permittivity of free space (ε0).

In this case, we can consider a cylindrical Gaussian surface with the point charge Q at its center and the conducting plate as its base. The flux through this surface is given by:

Φ = E * A = (kQ/r^2) * A

Where A is the area of the base of the cylinder.

Since the net electric field at the surface of the plate is zero, the flux through the surface is also zero. This means that the total charge enclosed by the surface must also be zero, which leads us to the conclusion that the total charge on the conductor is -Q.

In general, when solving problems involving point charges and conductors, it is important to consider the effects of the electric field and the induced charges on the conductor. Using Gauss's Law and the concept of electric fields, you can solve problems like this one.

I hope this explanation helps you understand this concept better. Let me know if you have any further questions. Good luck with your studies!