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E field Angle
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Bill Miller
science forum beginner


Joined: 24 Jun 2006
Posts: 4

PostPosted: Thu Jul 13, 2006 12:10 am    Post subject: E field Angle Reply with quote

Theoretically, the Electrical (E) field associated with a conductor is at
exactly 90 degrees with respect to that conductor.

It appears, however, that real conductors behave diffeeently and that the E
field associated with a real conductor is at an angle that is slightly
displaced from 90 degrees.

What are the parameters that govern this angle, and what is the range of
angles that is likely to be encountered with typical conductors such as Cu,
Al, Ag and others?What angular difference (if any) is there between a DC
field and an AC field with the same peak V/M amplitude?

Thanks!

Bill Miller
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Douglas Natelson
science forum beginner


Joined: 20 May 2005
Posts: 13

PostPosted: Fri Jul 14, 2006 6:52 pm    Post subject: Re: E field Angle Reply with quote

Bill Miller wrote:
Quote:
Theoretically, the Electrical (E) field associated with a conductor is at
exactly 90 degrees with respect to that conductor.

That's true for dc fields. The surface of the conductor is all at the
same potential (if it wasn't, current would start to flow to screen
out the potential differences). Since the E field is proportional
to the gradient of the potential, it has to be normal to the conducting
surface.

Quote:
It appears, however, that real conductors behave diffeeently and that the E
field associated with a real conductor is at an angle that is slightly
displaced from 90 degrees.

Only at nonzero frequencies.

Quote:
What are the parameters that govern this angle, and what is the range of
angles that is likely to be encountered with typical conductors such as Cu,
Al, Ag and others?What angular difference (if any) is there between a DC
field and an AC field with the same peak V/M amplitude?

The complex dielectric function as a function of frequency is really
what determines the boundary conditions. For truly dc fields,
the field is locally normal to the surface. Try reading up on
"skin depth" and related terms.

--DN
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Bergervoet dr. J.R.M.
science forum beginner


Joined: 26 Jun 2006
Posts: 2

PostPosted: Fri Jul 14, 2006 6:56 pm    Post subject: Re: E field Angle Reply with quote

Bill Miller wrote:
Quote:
Theoretically, the Electrical (E) field associated with a conductor is at
exactly 90 degrees with respect to that conductor.

Only for a perfect conductor, or for a DC field.

Quote:
It appears, however, that real conductors behave diffeeently and that the E
field associated with a real conductor is at an angle that is slightly
displaced from 90 degrees.

It is pointing slightly forward for an AC current, in a way that
gives a Poynting vector slightly inwards to the material. This inward
component of the energy flux corresponds to the losses in the material.

Quote:

What are the parameters that govern this angle, and what is the range of
angles that is likely to be encountered with typical conductors such as Cu,
Al, Ag and others?What angular difference (if any) is there between a DC
field and an AC field with the same peak V/M amplitude?

The inward energy flux vs. forward flux (from the Poynting vector) gives
you the angle. For a linear wire, for instance, you can easily integrate
the values. So it comes down to knowing the losses in the wire, compared
to the total AC power transported. I leave the details to you!

-- Jos

Quote:

Thanks!

Bill Miller
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Bill Miller
science forum beginner


Joined: 24 Jun 2006
Posts: 4

PostPosted: Sat Jul 15, 2006 5:31 am    Post subject: Re: E field Angle Reply with quote

Hello DN and thanks for the reply...

Actually I am interested in AC/RF performance when a current is flowing
through the conductor. (I'm sorry I did not mention that!)

.. I'm familiar with skin depth data and formulae, but the information
doesn't seem to be applicable to the E field angle (or I do not understand
how to interpret it in that way!)

The interface I am interested in is very simple -- metal -to - air (or
vacuum).

Bill Miller


"Douglas Natelson" <natelson@no-spam.rice.no-spam.edu> wrote in message
news:e95jfd$eah$1@joe.rice.edu...
Quote:
Bill Miller wrote:
Theoretically, the Electrical (E) field associated with a conductor is at
exactly 90 degrees with respect to that conductor.

That's true for dc fields. The surface of the conductor is all at the
same potential (if it wasn't, current would start to flow to screen
out the potential differences). Since the E field is proportional
to the gradient of the potential, it has to be normal to the conducting
surface.

It appears, however, that real conductors behave diffeeently and that the
E field associated with a real conductor is at an angle that is slightly
displaced from 90 degrees.

Only at nonzero frequencies.

What are the parameters that govern this angle, and what is the range of
angles that is likely to be encountered with typical conductors such as
Cu, Al, Ag and others?What angular difference (if any) is there between a
DC field and an AC field with the same peak V/M amplitude?

The complex dielectric function as a function of frequency is really
what determines the boundary conditions. For truly dc fields,
the field is locally normal to the surface. Try reading up on
"skin depth" and related terms.

--DN
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castanalysis@gmail.com
science forum beginner


Joined: 17 Jul 2006
Posts: 1

PostPosted: Mon Jul 17, 2006 3:32 pm    Post subject: Re: E field Angle Reply with quote

Dear Bill

Figure out your source conditions, solve the boundary value problem,
with Smyth's book on EM a very good reference for this problem. If
it is an induction source then the paper "Analytical Solutions to
Eddy-Current Probe-Coil Problems" Journal of Applied Physics Vol 39
p2829 (1968). Works for conductors only, not real ferromagnets.

J. Wallace

Bill Miller wrote:
Quote:
Hello DN and thanks for the reply...

Actually I am interested in AC/RF performance when a current is flowing
through the conductor. (I'm sorry I did not mention that!)

. I'm familiar with skin depth data and formulae, but the information
doesn't seem to be applicable to the E field angle (or I do not understand
how to interpret it in that way!)

The interface I am interested in is very simple -- metal -to - air (or
vacuum).

Bill Miller


"Douglas Natelson" <natelson@no-spam.rice.no-spam.edu> wrote in message
news:e95jfd$eah$1@joe.rice.edu...
Bill Miller wrote:
Theoretically, the Electrical (E) field associated with a conductor is at
exactly 90 degrees with respect to that conductor.

That's true for dc fields. The surface of the conductor is all at the
same potential (if it wasn't, current would start to flow to screen
out the potential differences). Since the E field is proportional
to the gradient of the potential, it has to be normal to the conducting
surface.

It appears, however, that real conductors behave diffeeently and that the
E field associated with a real conductor is at an angle that is slightly
displaced from 90 degrees.

Only at nonzero frequencies.

What are the parameters that govern this angle, and what is the range of
angles that is likely to be encountered with typical conductors such as
Cu, Al, Ag and others?What angular difference (if any) is there between a
DC field and an AC field with the same peak V/M amplitude?

The complex dielectric function as a function of frequency is really
what determines the boundary conditions. For truly dc fields,
the field is locally normal to the surface. Try reading up on
"skin depth" and related terms.

--DN
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Jos Bergervoet
science forum beginner


Joined: 16 Dec 2005
Posts: 5

PostPosted: Mon Jul 17, 2006 3:32 pm    Post subject: Re: E field Angle Reply with quote

Douglas Natelson wrote:
Quote:
Bill Miller wrote:

Theoretically, the Electrical (E) field associated with a conductor is at
exactly 90 degrees with respect to that conductor.

That's true for dc fields.

Actually, that should be "electrostatic fields", not dc fields! I made
the same 'typo' in my other reply. But a DC field could for instance
mean the field of a DC current through a wire, which has basically the
same forward component of the E-field to overcome the resistance.

So, it's only true for perfect conductors, or electrostatic fields. And
in the latter case not even exactly, due to the precise charge density
in the depletion/accumulation layer. It will fail near sharp corners.

-- Jos
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