# I'm interested in the idea of voltage

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

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.

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.