I'm interested in the idea of voltage

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    Idea Voltage
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Discussion Overview

The discussion centers on the concept of voltage, particularly in the context of electric fields and their behavior under varying conditions, such as time-varying magnetic fields. Participants explore the implications of curl and curvature of electric fields, the calculation of voltage between points, and the potential redefinition of circuit properties based on these factors.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant discusses the relationship between the curl of the electric field (E) and voltage, noting that when curl(E) = 0, voltage can be calculated as the line integral of E over a path.
  • Another participant suggests considering a closed surface, like a sphere, to understand the tangential nature of curl compared to divergence.
  • A participant describes their experience with a field solver that provides a vector-valued electric field and questions whether to account for both E and magnetic fields (B) in calculating circuit properties.
  • Concerns are raised about the implications of time-varying B fields on voltage calculations and the potential need to redefine capacitance and inductance based on these variations.
  • One participant questions the relevance of changing B fields in an electrostatics context, prompting further exploration of circuit analysis under AC conditions.
  • Another participant references a textbook that discusses high-frequency behavior in circuits where electrostatics may not hold, suggesting that voltage around a loop may not add up as expected.

Areas of Agreement / Disagreement

Participants express differing views on the relevance of time-varying magnetic fields in electrostatics and the implications for circuit analysis. There is no consensus on how to approach the calculation of voltage in the presence of these factors, indicating ongoing debate and exploration of the topic.

Contextual Notes

Participants acknowledge the complexity of the relationship between electric and magnetic fields, particularly under dynamic conditions. There are references to specific assumptions about the smallness of certain derivatives and the need for further clarification on the significance of curl in practical applications.

Who May Find This Useful

This discussion may be of interest to those studying electrical engineering, circuit analysis, or electromagnetic theory, particularly in contexts involving dynamic fields and their effects on circuit properties.

sanjoser
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I'm interested in the idea of voltage.
if the curl of E =0, then E = -grad(potential), and it's
possible to calculate the voltage between two points
as the line integral of E over some path.
When there's a time changing magnetic induction, the
curl of E = -d(B)/dt. so strictly speaking the idea of voltage
gets a little unclear.
I don't have a lot of intuition about curl and the curvature
of electric field. It seems to me that it's possible to express
an electric field in a power series of (scale_length*frequency),
but I'd like to know if there's a way to calculate the curvature of
electric field and use that to modify the idea of voltage.
I think this might have application to calculating an equivalent
circuit description of a physical device from a field solver
 
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sanjoser said:
I don't have a lot of intuition about curl and the curvature
of electric field.

First, you have to think of a closed surface - I prefer a sphere.

The curl is everywhere tangential to the sphere (whereas divergence is perpendicular).

I think this might have application to calculating an equivalent
circuit description of a physical device from a field solver

If you have access to IEEE papers, you might try looking for a paper (circa 1978) by Dr H. Thal regarding an exact circuit analysis of spherical waves.

Regards,

Bill
 


well, that's not quite what I'm looking for.
The circumstance is that I've run a field solver on some presumably electrically small
device and I have a vector valued electric field in each element.
if I want to calculate the voltage between two points, I'd traverse an arbitrary path
between the points and add up the electric fields suitably along the path.
now on one hand, the field solution has decoupled the E & B fields and done
a soution based on electrostatics, assuming either that the time derivative of B
is small, or the curl of E is small, depending on how you look at it.
I'm trying to decide if I should solve for both E & B and try to correct the calculated
circuit properties for both of them.
this would lead to a redefinition of capacitance, as the voltage between two points
would depend on the time derivative iof B, and a redefinition of inductance somehow.
I'd like to calculate the curl of E along a path and decide if it's small enough to
ignore, but I don't have any feel for what's big or small, or how to calculate it.
I appreciate the opportunity to write this down, as it's helped my thoughts a lot,
and I'm happy to hear any opinions.
 


sanjoser said:
I appreciate the opportunity to write this down, as it's helped my thoughts a lot,
and I'm happy to hear any opinions.

If this is an electrostatics problem, why would the B fields be changing with time?

Regards,

Bill
 


an ac analysis of a lumped circuit has time variation. determination of the circuit
properties is done using electrostatics to calculate voltages, resistances and capacitances,
and magnetostatics to calculate inductances and loop currents. There are simple circuits that
have high frequency behavior without guided waves where you can observe violations
of electrostatics, like the voltages around a loop don't add up. Look at the textbook "Electromagnetic Fields and Energy" by Haus & Melcher.
 

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