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Penetration depth of quasi-static H -field into a conductor

Penetration depth of quasi-static H -field into a conductor. Section 59. Consider a good conductor in an external periodic magnetic field. The conductor is penetrated by the H -field, which induces a variable E-field, w hich causes “eddy” currents.

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Penetration depth of quasi-static H -field into a conductor

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  1. Penetration depth of quasi-static H-field into a conductor Section 59

  2. Consider a good conductor in an external periodic magnetic field The conductor is penetrated by the H-field, which induces a variable E-field, which causes “eddy” currents.

  3. Penetration of field is determined by the thermal conduction equation

  4. Quiz: How does the propagation of heat depend on time? • Linearly • Quadratic • Square root

  5. Quiz: How does the skin depth depend on frequency? • Inverse • Square root • Inverse Square root

  6. E-field inside conductor in high frequency limit

  7. Wavelength in metal is d not l, but d is also the characteristic damping length. Not much of a wave!

  8. Quiz: At a given position within a conductor the low frequency limit, how does the electric field depend on frequency? • Increases linearly with f. • Increases as the square root of f. • Decreases as the inverse square root of f.

  9. At a given position within a conductor the high frequency limit, how does the electric field depend on frequency? • Increases as Sqrt[f] • Decreases as Exp[-const*Sqrt[f]] • Decreases as Sqrt[f] *Exp[-const*Sqrt[f]]

  10. High frequency electric field in a conductor

  11. Eddy currents dissipate field energy into Joule heat

  12. Quiz: In low frequency fields, how does the rate of Joule heating for a metal depend on frequency? • Decreases as inverse square root of f • Increases linearly in f • Increases as f2

  13. In high frequency fields, how does the rate of Joule heating for a metal depend on frequency? • Increases as square root of f • Decreases as 1/f • Increases as f2

  14. A conductor acquires a magnetic moment in a periodic external H-field with the same period.

  15. Quiz: What is a possible frequency dependence for the electric field at a given point inside a metal? .P

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