Applying the divergence theorem to find total surface charge

In summary, the divergence theorem is a mathematical principle that relates the surface integral of a vector field over a closed surface to the volume integral of the divergence of the same vector field over the enclosed volume. It can be applied to find total surface charge by converting the surface charge density into a vector field and using the surface integral over a closed surface. Surface charge density is a measure of the amount of charge present per unit area on a surface. The main assumptions for using the divergence theorem to find surface charge are that the charge distribution is continuous, the surface is closed and encloses a volume, and the electric field is well-behaved. It can be applied to any shape or surface as long as these assumptions are met.
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Physgeek64
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Homework Statement


Sorry- I've figured it out, but I am afraid I don't know how to delete the thread.

Thank you though :)

Homework Equations


Below

The Attempt at a Solution


Photo below- I promise its coming! I've started by using cylindrical coordinates, but I wasn't sure if spherical coordinates would be better? Ill attach my photo below, but I'm stuck as to where to go from here. Many thanks in advance, I promise the photo is coming- I just don't know how to attach it on this section
 
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Related to Applying the divergence theorem to find total surface charge

1. What is the divergence theorem?

The divergence theorem, also known as Gauss's theorem, is a mathematical principle that relates the surface integral of a vector field over a closed surface to the volume integral of the divergence of the same vector field over the enclosed volume.

2. How can the divergence theorem be applied to find total surface charge?

The divergence theorem can be applied to find the total surface charge by first converting the surface charge density into a vector field. Then, the surface integral of this vector field over a closed surface will give the total surface charge enclosed within that surface.

3. What is meant by surface charge density?

Surface charge density is a measure of the amount of charge present per unit area on a surface. It is typically denoted by the symbol σ and has units of coulombs per square meter (C/m²).

4. What are the assumptions made when using the divergence theorem to find surface charge?

The main assumptions when using the divergence theorem to find surface charge are that the charge distribution is continuous, the surface is closed and encloses a volume, and the electric field is well-behaved and can be described by a vector field.

5. Can the divergence theorem be applied to any shape or surface?

Yes, the divergence theorem can be applied to any shape or surface as long as the assumptions mentioned in question 4 are satisfied. It is a general principle that can be used to find surface charge for various geometries, including spheres, cubes, and more complex surfaces.

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