Gauss's Law - electric flux through a spherical shell

In summary, to determine the total electric flux through a spherical shell of radius 4 m placed in a uniform electric field with magnitude 7020 N/C, use Gauss's Law and multiply the electric field strength by 4πr^2. However, if there is no charge enclosed inside the shell and the only electric field is caused by a charge distribution outside the shell, Gauss's Law states that the total electric flux through the shell will be zero.
  • #1
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Homework Statement



A spherical shell of radius 4 m is placed in a uniform electric field with magnitude
7020 N/C. Determine the total electric flux through
the shell. Answer in units of N · m^2/C.

Homework Equations



Gauss's Law

The Attempt at a Solution



I thought this would be as simple as E * 4[tex]\pi[/tex]r[tex]^{2}[/tex] , but it's not working

I did 7020 * 4[tex]\pi[/tex]*4[tex]^{2}[/tex] and got 1411454.747, which isn't right. Is there something more to the problem that I'm missing?
 
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  • #2
Is there any charge enclosed inside the shell? If there is no charge inside the shell, and the only electric field of concern is caused by some sort of charge distribution outside the shell, what does Gauss' law say about that?
 

What is Gauss's Law and how does it relate to electric flux through a spherical shell?

Gauss's Law is a fundamental law in electromagnetism that relates the electric flux through a closed surface to the net charge enclosed within that surface. This law can be applied to calculate the electric flux through a spherical shell, where the electric field is constant and perpendicular to the shell's surface.

What is electric flux and how is it calculated through a spherical shell?

Electric flux is a measure of the amount of electric field passing through a given surface. To calculate the electric flux through a spherical shell, we use the formula Φ = E ∙ A, where Φ is the electric flux, E is the electric field, and A is the area of the spherical shell.

How does the charge distribution affect the electric flux through a spherical shell?

The charge distribution within the spherical shell does not affect the electric flux through the shell. This is because the electric field is constant and perpendicular to the surface, so the amount of electric flux passing through the shell remains the same regardless of the charge distribution.

What is the relationship between the electric flux and the charge enclosed within a spherical shell?

According to Gauss's Law, the electric flux through a closed surface is equal to the net charge enclosed by that surface divided by the permittivity of free space (ε0). This means that the electric flux through a spherical shell is directly proportional to the charge enclosed within the shell.

Can Gauss's Law be applied to other shapes besides a spherical shell?

Yes, Gauss's Law can be applied to any closed surface, including cubes, cylinders, and irregular shapes. The key is to choose a surface where the electric field is constant and perpendicular to the surface.

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