Conductor with a charge problem

[STP]

Hey everyone, first post and having an issue thinking about a simple problem. I'm into chemistry so I struggle to get all of these physics ideas down correctly.

The problem is about a conductor with a neutral surface. The conductor has a cavity with a point charge of +P inside of it. A charged rod transfer -q to the conductor.

My issue is finding the charge on the inner wall of the conductor's cavity. My book doesn't describe a transfer of this sort and just says the inner wall of the cavity has to cancel out the point charge.

Thanks

 

[Shooting Star]

Surround the cavity by a Gaussian surface S lying inside the conductor. Inside a conductor, the field is always zero. The closed surface integral over S, integral E.da = 0, since E = 0 at every point. What do you think the induced charge on the cavity wall should be using Gauss’ law?

 

[Moetasim]

for your post and welcome to the scientific community! Your problem is a common one and it's great that you're reaching out for help. As a scientist, it's important to remember that we all face challenges and it's okay to ask for assistance.

In regards to your problem, it's important to understand the principles of charge transfer and how it affects conductors. In this scenario, the charged rod is transferring a negative charge to the neutral conductor. This will cause the electrons in the conductor to redistribute, creating an electric field within the conductor. As the electrons move, they will eventually reach equilibrium and the electric field will become zero.

Now, in order for the inner wall of the cavity to cancel out the point charge, it must have an equal and opposite charge. This means that the negative charge transferred from the rod must be distributed evenly on the inner wall of the cavity. This is known as charge induction, where the presence of a charged object influences the distribution of charges in a conductor.

To find the charge on the inner wall of the cavity, you can use the principle of charge conservation. This states that the total charge in a closed system remains constant. In this case, the total charge in the conductor and the cavity must be equal to the charge on the rod, which is -q. Therefore, the charge on the inner wall of the cavity will also be -q.

I hope this helps to clarify the problem and guide you in finding the solution. Remember, as a scientist, it's important to approach problems with patience and a willingness to learn. Keep exploring and questioning, and you will continue to grow as a scientist. Best of luck!