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- Homework Statement
- The title of this section is "Charge Distributions with Enough Symmetry for Gauss's Law"

The problem is stated as follows:

On which of the objects shown in the figure above can you apply Gauss's Lw to find the Electric Field from the given charge density? (Choose all that apply, see picture below)

1. Infinite line of charge with a uniform charge density ##\lambda_0##

2. Infinite cylinder of charge with charge density ##\rho=\rho_0\frac{\cos{\theta}}{r}##

3. A slab of charge, infinite in ##y## an ##z## with a constant charge density ##\rho##

4. A ring of charge with uniform charge density ##\lambda_0##

5. A sphere with uniform charge density ##\rho_0##

- Relevant Equations
- As far as I can tell, you could in theory apply Gauss's Law to any of the objects in the figure below. This answer, according to the automated answer from MIT Open Library, is incorrect.

Calculating the flux of the electric field generated by a charge distribution can be made easier or harder depending on the Gaussian surface chosen. However, as long as we can calculate the flux of the electric field through a closed surface, we can apply Gauss's Law. Is this true?

In the case of the infinite line and cylinder, we use as Gaussian surface a cylinder with end-caps perpendicular to the line or cylinder.

For the infinite slab, we can use a cylinder with the shaft of the cylinder perpendicular to the slab.

For the ring, we could use a piece of a torus around a small piece of the ring.

For the solid sphere we use an enclosing sphere.

**What am I missing?**

I also don't get the title of the section: "Charge distributions with enough symmetry for Gauss's Law".

I thought Gauss's Law was valid for any closed surface enclosing a charge. I don't understand what "enough symmetry" means in the title above. I get that with symmetry it's easier to solve the integrals involved by hand.