Maxwell Stress Tensor Homework: Find E & B Field Components

In summary, the problem involves calculating the Maxwell stress tensor at a midway point between two nonconducting cylindrical shells surrounding long wires carrying current in opposite directions. The x shell has a positive charge per unit length while the y shell has a negative charge per unit length. The necessary equations for calculating the stress tensor are provided, but the question is how to find the i and j components of the electric and magnetic fields. The person asking the question is directed to review examples of calculating these fields for simple charge distributions.
  • #1
tomfrank
38
0

Homework Statement


x and y are nonconducting cylindrical shells. Both cylindrical shells are surrounding long wires that are carrying current. the x shell out of the page and the y shell into the page.
x radius has a charge per unit length = to +[tex]\lambda[/tex]
y radius has a charge per unit length = to -[tex]\lambda[/tex]
I need to calculate the maxwell stress tensor at a midway between x and y. (from the picture)

Homework Equations



Tij =[tex]\epsilon[/tex]o(EiEj-[tex]\delta[/tex]ijE2)+(1/[tex]\mu[/tex])(BiBj-[tex]\delta[/tex]ijB2)

The Attempt at a Solution



How do I exactly found the i and j component of the magnetic and electric field?
 
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  • #2
can anyone help me?
 
  • #3
If you're studying the Maxwell stress tensor, you should already know how to calculate the electric and magnetic fields of simple charge distributions...surely you've already seen examples that include the magnetic field of a long straight current carrying wire and the electric field of a uniformly charged cylindrical shell?
 
  • #4
i got the problem..thanks bye
 

1. What is the Maxwell Stress Tensor and why is it important?

The Maxwell Stress Tensor is a mathematical tool used in electromagnetism to calculate the stress exerted by an electric or magnetic field on a material. It is important because it allows us to understand how electric and magnetic fields interact with matter and can be used to predict the behavior of materials under these fields.

2. How do you calculate the components of the E and B fields using the Maxwell Stress Tensor?

The components of the E and B fields can be calculated using the Maxwell Stress Tensor through the equations:
Ei = (1/ε0) * ∂Tij/∂xj
Bi = (1/μ0) * ∂Tij/∂xj,
where Tij is the components of the Maxwell Stress Tensor, ε0 is the permittivity of free space, and μ0 is the permeability of free space.

3. What are the units of the Maxwell Stress Tensor?

The units of the Maxwell Stress Tensor are normally expressed in terms of force per unit area, such as N/m2 or Pa. However, the units may vary depending on the system of units being used.

4. Can the Maxwell Stress Tensor be used to calculate the stress on any material?

Yes, the Maxwell Stress Tensor can be used to calculate the stress on any material as long as the material is linearly elastic and does not exhibit any significant magnetic properties. This means that the stress on non-linear or magnetic materials cannot be accurately calculated using the Maxwell Stress Tensor.

5. Are there any limitations to using the Maxwell Stress Tensor?

One limitation of the Maxwell Stress Tensor is that it only takes into account the stress caused by electric and magnetic fields. Other factors such as thermal stress or mechanical stress may also affect the behavior of materials but are not considered in this calculation. Additionally, the Maxwell Stress Tensor assumes that the material is isotropic, meaning its properties are uniform in all directions, which may not always be the case in real-world materials.

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