Draw the field for two concentric conducting spheres

• Indigo
In summary: The outer shell has the same effect as the inner shell. The field point is located at the center of the spheres.
Indigo

Homework Statement

We are given two concentric conducting shells centered around a common origin. Within the inner shell there is a positive point charge q and somewhere outside the two shells is another positive point charge q. The question wants the field lines for this system and then again for the same system with a wire connecting the two conducting shells

Homework Equations

I'm pretty sure I don't need any equations for this one.

The Attempt at a Solution

What I have currently is in the attached photo. I'm nearly sure this is wrong though because they can't be the same can they?
I don't really get how having two shells makes the first system any different than having one shell.

If you wouldn't mind taking a look and telling me if I'm on the right track or not that would be great!
Thank You!

Attachments

• concentric spheres.png
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You are not far off. I don't know if you have been acquainted with Gauss's law already? Makes this a simple exercise.

I take for granted that the spheres themselves are neutral. So the positive charge inside pulls the negative charge to the inside of the inner sphere and there remains a positive charge on the outside of the inner sphere. Has to be evenly distributed (because it is a conductor). Same story for the outside shell in the upper picture. So you draw radial field lines between the shells. Net result for the outside world indistinguishable from a positive charge at the center of the spheres. So the 0 field point should be half way (you draw it a bit to the right).

In the bottom figure the wire ensures there is no field between the spheres (otherwise the potential difference over the wire would conduct charge until same potential).
Net result to the outside world same as in top figure: a charge at the center of the spheres.

Sketchy field lines at the left should - close to the sphere - be perpendicular to the surface: there can be no component parallel to the surface -- it's a conductor!

Okay, that makes a lot of sense! I guess I didn't really think of how the wire was affecting the field. When you have two conductors connected by a wire can you almost think of the as one thick shell? Since there can never be a field inside a solid conductor?

Thank you!

1. What is the purpose of drawing the field for two concentric conducting spheres?

The purpose of drawing the field for two concentric conducting spheres is to visualize the electric field lines and understand the distribution of electric charge and potential between the two spheres. It is also useful for calculating the electric field strength at different points between the spheres.

2. How do the electric field lines look like for two concentric conducting spheres?

The electric field lines for two concentric conducting spheres will be radial lines originating from the inner sphere and terminating on the outer sphere. These lines will be evenly spaced and perpendicular to the surface of the spheres.

3. What factors affect the electric field between two concentric conducting spheres?

The electric field between two concentric conducting spheres is affected by the difference in charge between the spheres, the distance between them, and the dielectric constant of the medium between the spheres. It is also influenced by the size and shape of the spheres.

4. How can the electric field strength be calculated between two concentric conducting spheres?

The electric field strength between two concentric conducting spheres can be calculated using Coulomb's law, which states that the electric field strength is directly proportional to the product of the charges on the spheres and inversely proportional to the square of the distance between them.

5. What are some practical applications of understanding the field for two concentric conducting spheres?

Understanding the field for two concentric conducting spheres has practical applications in various fields, such as in the design of capacitors, particle accelerators, and high-voltage equipment. It also helps in understanding the behavior of charged particles in electric fields and in the study of electromagnetic radiation.

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