How Do You Calculate the Maxwell Stress Tensor Between Cylindrical Shells?

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SUMMARY

The discussion focuses on calculating the Maxwell Stress Tensor between two nonconducting cylindrical shells surrounding long wires carrying current. The outer shell (x) has a charge per unit length of +λ, while the inner shell (y) has a charge per unit length of -λ. The relevant equation for the Maxwell Stress Tensor is given as Tij = ε₀(EiEj - δijE²) + (1/μ)(BiBj - δijB²). Participants seek guidance on determining the i and j components of the electric and magnetic fields at the midpoint between the two shells.

PREREQUISITES
  • Understanding of Maxwell's equations
  • Familiarity with electric and magnetic fields in cylindrical coordinates
  • Knowledge of the Maxwell Stress Tensor formulation
  • Basic principles of electrostatics and magnetostatics
NEXT STEPS
  • Study the derivation of the Maxwell Stress Tensor in cylindrical coordinates
  • Learn how to calculate electric fields generated by charged cylindrical shells
  • Explore the calculation of magnetic fields around current-carrying wires
  • Investigate the application of the divergence theorem in electromagnetic contexts
USEFUL FOR

This discussion is beneficial for physics students, electrical engineers, and researchers focusing on electromagnetic theory, particularly those interested in the behavior of electric and magnetic fields in cylindrical geometries.

tomfrank
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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 +\lambda
y radius has a charge per unit length = to -\lambda
I need to calculate the maxwell stress tensor at a midway between x and y. (from the picture)

Homework Equations



Tij =\epsilono(EiEj-\deltaijE2)+(1/\mu)(BiBj-\deltaijB2)

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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can anyone help me?
 

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