Electric fields and Frozen charges

[limonysal]

Electric fields and "Frozen charges"

Homework Statement

A large parallel plate capacitor is charged at first and creates a uniform electric field inside which is to the right and of magnitued E₀. Then a small metal box is inserted inside the capacitor; small means that the insertion does not modify the charge distribution on the capacitor. This will make the field inside the metal box zero (Faraday cage). Now imagine you could somehow freeze or nail down all charges in the entire system and then remove the metal box with all its frozen charges far away from the capacitor.

Draw a picture that shows what the electric field looks like 1. inside the hollow of the box, b. inside the body of the box, and c. outside the bow. (THe principle of superposition is helpful).

The Attempt at a Solution

My first thoughts when I saw this were that you would generate an electric field going from one side of the box to the other. But...since the box is metal (so a conductor), the charges would rearrange themselves and the box would become neutral, and there would be no electric field. Would there?

Also...it says that the charges are frozen...would you take this to be that half of the box remains positively charged and half of it remains negatively charged? If so, how would you draw that...lines curving inward from one side inside the gap? and outward on the outside?
This might be asking a bit much...I could try to post the original image but I'm not sure how.

 

[AvroArrow]

1. Inside the hollow of the box: no electric field2. Inside the body of the box: no electric field (due to the frozen charges balancing each other out)3. Outside the box: an electric field pointing to the right with a magnitude of E0 (due to the original electric field from the capacitor).

 

[nlightner]

I would like to clarify a few things about the concept of electric fields and "frozen charges" in this scenario.

Firstly, electric fields are not physical objects that can be frozen or nailed down. They are a property of space that is created by the presence of electric charges. So, the idea of "freezing" electric fields is not scientifically accurate.

Secondly, a Faraday cage does not eliminate the electric field inside it. It simply redistributes the charges on its surface in a way that cancels out the external electric field. So, the electric field inside the metal box would not be zero, but it would be significantly reduced.

In this scenario, if we assume that the metal box is inserted perfectly in the center of the capacitor, the electric field inside the hollow of the box would be zero, as the charges on the inner surface of the box would cancel out the electric field from the capacitor. The electric field inside the body of the box would also be zero, as the charges on the outer surface of the box would cancel out the electric field from the capacitor. However, there would still be an external electric field from the capacitor, which would be unaffected by the presence of the metal box.

As for the charges being "frozen", it is important to note that electric charges are not physical objects that can be frozen in place. They are constantly in motion and can only be "frozen" in a figurative sense. In this scenario, it is likely that the charges on the inner and outer surfaces of the metal box would redistribute themselves to cancel out the electric field from the capacitor, but it would not be accurate to say that they are "half positively charged and half negatively charged". The distribution of charges would depend on the exact geometry and placement of the metal box in the capacitor.

Overall, I would caution against using the term "frozen charges" in a scientific context, as it can be misleading and inaccurate. Instead, it would be more accurate to say that the charges have redistributed themselves to cancel out the electric field. I hope this explanation helps clarify the concept of electric fields and "frozen charges" in this scenario.