Electromagnetic fields in a circuit?

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SUMMARY

This discussion centers on the behavior of electromagnetic (EM) fields in circuits, particularly in the context of perfect conductors. It clarifies that while E and B fields are zero within a perfect conductor, voltage can still appear across a resistor when connected to an ideal DC voltage source. The conversation highlights the presence of ambient magnetic fields that can induce voltage across circuit components, emphasizing the importance of understanding transmission lines and their associated parameters, such as inductance and characteristic impedance.

PREREQUISITES
  • Maxwell's equations
  • Understanding of perfect conductors
  • Knowledge of transmission lines and the telegrapher's equation
  • Familiarity with inductance and capacitance in circuits
NEXT STEPS
  • Study the implications of Maxwell's equations in circuit theory
  • Research the behavior of voltage and current in perfect conductors
  • Learn about the telegrapher's equation and its applications in transmission lines
  • Explore the formulas for inductance in various coil geometries
USEFUL FOR

Electrical engineers, physics students, and anyone interested in the principles of electromagnetic fields in circuits and transmission line theory.

HydroGuy
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I'm having some trouble getting a good understanding of how the EM fields are working in a circuit. Essentially, Maxwell's equations and boundary conditions at a perfect conductor are confusing me.

If, in a perfect conductor, the E and B fields are zero, then how does a voltage appear in a circuit? IE, if we attached an ideal DC voltage source to a loop of perfect conductor with a resistor in the middle, then if there is no E or B in the loop, is there a voltage at the resistor?

Any references to understanding the fields when DC and AC are applied to a t-line or circuit would be very helpful.
 
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Even a perfectly conducting straight wire has external magnetic fields. So a straight wire has inductance. A coil has a lot more. In this link, here are formulas for a variety of coil geometries.
http://en.wikipedia.org/wiki/Inductor.
In a coaxial transmission line, the center conductor has series inductance L per unit length and shunt capacitance C (to the outer conductor) per unit length. The characteristic impedance Z of a coaxial transmission line is
Z = sqrt(L/C) ohms

Bob S
 
If you had a loop of a perfectly conducting wire looping around from one resister terminal to the other, ambient magnetic fields will induce a voltage across the resistor.

Any current, ac or dc, in a circuit loop, will have a magnetic field in its center.

A long straight perfectly conducting wire carrying a current will have a magnetic field surrounding the wire.

Magnetic fields are anywhere there are currents.

Magnetic fields exist between the inner and outer conductors of transmission lines.

Read about transmission lines and the telegrapher's equation in

http://en.wikipedia.org/wiki/Transmission_line

Bob S
 
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