Gauss's Law with a sphere on and charge on z-axis

In summary, Gauss's Law is a fundamental law in electromagnetism that relates the electric flux through a closed surface to the net electric charge enclosed by that surface. When a charged sphere is placed on the z-axis, the electric flux through a spherical surface centered on the sphere will depend on the magnitude of the charge and the distance from the center of the sphere. The formula for Gauss's Law with a sphere and charge on the z-axis is given by Φ<sub>E</sub> = Q<sub>enc</sub> / ε<sub>0</sub>, where Φ<sub>E</sub> is the electric flux, Q<sub>enc</sub> is the net enclosed charge, and ε<sub
  • #1
ScandelousWenc
1
0
I have a question for E&M and I feel like I am over complicating it. As the title says, the is a positive charge on the x-axis and I must prove that flux = q/εo.

Since the charge is on the z-axis, could I just add in a term (z-z') to account for the charge not being at the origin into calculating ∫E dA?
 
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  • #2
Welcome to PF;
If you already know an equation is f(x,y,z), then shifting the source a distance z' in the +z direction turns that into f(x,y,z-z') yes.
 

1. What is Gauss's Law with a sphere and charge on the z-axis?

Gauss's Law is a fundamental law in electromagnetism that relates the electric flux through a closed surface to the net electric charge enclosed by that surface. When a charged sphere is placed on the z-axis, the electric flux through a spherical surface centered on the sphere will depend on the magnitude of the charge and the distance from the center of the sphere.

2. What is the formula for Gauss's Law with a sphere and charge on the z-axis?

The formula for Gauss's Law with a sphere and charge on the z-axis is given by ΦE = Qenc / ε0, where ΦE is the electric flux, Qenc is the net enclosed charge, and ε0 is the permittivity of free space.

3. How does the electric field vary with distance from the charged sphere on the z-axis?

The electric field decreases with distance from the charged sphere on the z-axis according to the inverse square law. That is, the electric field is strongest close to the sphere and gets weaker as the distance increases.

4. How does the presence of other charges affect Gauss's Law with a sphere and charge on the z-axis?

According to Gauss's Law, the electric flux through a closed surface only depends on the net enclosed charge. Therefore, the presence of other charges outside of the surface will not affect the electric flux or the calculation of the electric field at a specific point on the surface.

5. Can Gauss's Law be used to calculate the electric field for any shape of charge distribution?

No, Gauss's Law can only be used to calculate the electric field for charge distributions with spherical symmetry. For other shapes of charge distributions, other methods, such as Coulomb's Law or the superposition principle, must be used to calculate the electric field.

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