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Old Aug 18th 2013, 01:28 AM   #1
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Magnetic field around wire with AC current

Hello,
I would appreciate any help with regard to the following question.
I have an infinitely long and thin wire with a curent passing through it. The current can be described with the equation:
i(t) = A*sin(2*PI*f*t).

What will be the magnetic field at a distance r from the wire?

I've heard the magnetic field will have two components.
The first one will be due to the current passing through the wire and it will vary with time:
B(t) = (u0 / 2*PI)*A*sin(2*PI*f*t)/r


And the second component will be caused by the displacement current.
Does anyone have any idea as how that second component can be described?

Last edited by dontmind; Aug 18th 2013 at 01:39 AM.
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Old Dec 12th 2013, 05:01 AM   #2
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Originally Posted by dontmind View Post
Hello,
I would appreciate any help with regard to the following question.
I have an infinitely long and thin wire with a curent passing through it. The current can be described with the equation:
i(t) = A*sin(2*PI*f*t).

What will be the magnetic field at a distance r from the wire?

I've heard the magnetic field will have two components.
The first one will be due to the current passing through the wire and it will vary with time:
B(t) = (u0 / 2*PI)*A*sin(2*PI*f*t)/r


And the second component will be caused by the displacement current.
Does anyone have any idea as how that second component can be described?
Your fine as is. The displacement current is the product of the permittivity and the electric field intensity summed with the polarization of the medium. In your case with an infinitely long conducting wire there is no displacement current. Think of a capacitor. As electron flow, current as we most know it, comes onto one plate it "displaces" free electrons from the other plate. This is done slightly out of time (usually said out of phase) with respect to the applied voltage driving the current. In this case the current flow through the dielectric is this displacement current. It typically aligns dipoles within the dielectric with the E field between the two plates but no actual free charges move through the dielectric.
Displacement current is reserved for energy flow per unit time through a dielectric as far as I know and no energy per unit time is displaced out of phase within a conductive wire.
So you're fine with the single function you have.
Many smiles,
Craig

Last edited by clombard1973; Dec 12th 2013 at 05:11 AM. Reason: typo
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Old Dec 12th 2013, 09:22 AM   #3
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Originally Posted by clombard1973 View Post
Your fine as is. The displacement current is the product of the permittivity and the electric field intensity summed with the polarization of the medium. In your case with an infinitely long conducting wire there is no displacement current. Think of a capacitor. As electron flow, current as we most know it, comes onto one plate it "displaces" free electrons from the other plate. This is done slightly out of time (usually said out of phase) with respect to the applied voltage driving the current. In this case the current flow through the dielectric is this displacement current. It typically aligns dipoles within the dielectric with the E field between the two plates but no actual free charges move through the dielectric.
Displacement current is reserved for energy flow per unit time through a dielectric as far as I know and no energy per unit time is displaced out of phase within a conductive wire.
So you're fine with the single function you have.
Many smiles,
Craig
Inductive reactance can also be ignored as the wire has no cross section. Are we to assume that the wire is straight?
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