Hollow Sphere with Uniform Surface charge

In summary, the conversation discusses the use of Poynting's Theorem and the equation for momentum in relation to a hollow sphere. The strategy is to treat the sphere as a point charge and use Gauss' Law to calculate the electric field. The magnetic field is calculated using the formula B = 2/3μ0M, where M is the magnetic dipole moment per unit volume. The question is whether this approach is correct for determining the total electromagnetic momentum, and if the E and B field equations are accurate. The attachment shows the current attempt at solving part A.
  • #1
woprxcpe1704tks
3
0

Homework Statement


Doc Feb 06, 2016, 12:42 copy.jpg
[/B]

Homework Equations


Poynting's Theorem S = 1/μ0 (E x B)
Momentum = p = μ0ε0 ∫ S dτ

The Attempt at a Solution


My strategy was to treat the hollow sphere as a point charge (by Gauss' Law), so E = 1/4πε0 Q/a2. I believe the magnetic field would be B = 2/3μ0M (where M is the magnetic dipole moment per unit volume). For part A, would this be the correct total electromagnetic momentum if I used the formula stated above and the relevant E and B fields. Also, do I have the E and B field formula's correct?
 
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  • #2
woprxcpe1704tks said:

Homework Statement


View attachment 95437 [/B]

Homework Equations


Poynting's Theorem S = 1/μ0 (E x B)
Momentum = p = μ0ε0 ∫ S dτ

The Attempt at a Solution


My strategy was to treat the hollow sphere as a point charge (by Gauss' Law), so E = 1/4πε0 Q/a2. I believe the magnetic field would be B = 2/3μ0M (where M is the magnetic dipole moment per unit volume). For part A, would this be the correct total electromagnetic momentum if I used the formula stated above and the relevant E and B fields. Also, do I have the E and B field formula's correct?

The attachment is my current attempt at part A
 

Attachments

  • Doc Feb 07, 2016, 11_23.pdf
    447.3 KB · Views: 232

1. What is a hollow sphere with uniform surface charge?

A hollow sphere with uniform surface charge is a three-dimensional object with a thin, hollow shell and a uniform distribution of electric charge on its surface. The charge is evenly spread out on the surface of the sphere, resulting in a symmetrical electric field both inside and outside of the sphere.

2. How is the electric field inside a hollow sphere with uniform surface charge calculated?

The electric field inside a hollow sphere with uniform surface charge is calculated using the Gauss's law. This law states that the electric field at any point inside a closed surface is equal to the total enclosed charge divided by the permittivity of free space. In the case of a hollow sphere with uniform surface charge, the electric field inside is zero, as the enclosed charge is also zero.

3. What is the relationship between the electric field and surface charge density of a hollow sphere?

The electric field and surface charge density of a hollow sphere are directly proportional. This means that as the surface charge density increases, the electric field also increases. Conversely, as the surface charge density decreases, the electric field decreases.

4. What is the significance of a hollow sphere with uniform surface charge in electrostatics?

A hollow sphere with uniform surface charge is significant in electrostatics because it is an example of a system with spherical symmetry. This makes it easier to calculate the electric field and potential at any point inside or outside of the sphere. It is also a common model used to understand the behavior of charged particles in a symmetrical system.

5. How does the presence of an inner charge affect the electric field of a hollow sphere with uniform surface charge?

If an inner charge is present inside the hollow sphere with uniform surface charge, the electric field inside the sphere will no longer be zero. The presence of the inner charge will create an electric field that is not uniform and will vary depending on the location inside the sphere. However, the electric field outside the sphere will remain the same as that of a hollow sphere with uniform surface charge.

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