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- TL;DR Summary
- 1.Straight conductor has an AC current running through it which makes alternating magnetic field

2.Next to it is a coreless coil

-How to calculate voltage induced at the ends of the coil if it's stationary?

-How to calculate voltage induced at the ends of the coil if it's moving alongside the straigh conductor?

So, as it says in the title, I am trying to calculate overall voltage induced in a coreless coil in the cases of it being stationary and moving in an alternating magnetic field. To go more into detail, I would like to create a mathematical model of a coil in an alternating magnetic field that emenates (for this purpose) from a straight, infinite conductor. The prospect of the coil moving in an already alternating magnetic field makes this calculation seem quite tricky to do (to me at least), and I was unable to find definitive answers both on the internet and in the books.

The questions are:

-How to calculate voltage induced at the ends of the coil if the coil is stationary in the alternating magnetic field of a straight conductor?

-How to calculate the voltage if the field is alternating and the coil is MOVING alongside the straight conductor?

The problems I'm facing are accounting for the very harsh weakening of a magnetic field with distance. Even if the coil has a diameter of couple of cm, there is a big disparity in magnetic field strength between the near and far side of the coil (relative to the straight conductor). Also, I am kind of confused by thinking about Faradays law in AC environment and the interaction with the moving coil.

Sidequestion: If I were to move the coil physically, how would i calculate the physical resistance it generates cause of repelling magnetic fields?

My attempt(EDIT1):

d1=distance from the straight conductor to the near side of the coil

d2=distance from the straight conductor to the far side of the coil

B1=(μ0∗I)/(2∗π∗d1)

B2=(μ0∗I)/(2∗π∗d2)

Bavg=(B1+B2)/2

I would reduce it by 30% because of radial nature of the magnetic field which weakens linearily with distance and the coil which overlaps with the magnetic field so:

Bavg=0,7*(B1+B2)/2

and finally

Ep=A*N*B*2*π*f

Erms=Ep/sqrt(2)

The questions are:

-How to calculate voltage induced at the ends of the coil if the coil is stationary in the alternating magnetic field of a straight conductor?

-How to calculate the voltage if the field is alternating and the coil is MOVING alongside the straight conductor?

The problems I'm facing are accounting for the very harsh weakening of a magnetic field with distance. Even if the coil has a diameter of couple of cm, there is a big disparity in magnetic field strength between the near and far side of the coil (relative to the straight conductor). Also, I am kind of confused by thinking about Faradays law in AC environment and the interaction with the moving coil.

Sidequestion: If I were to move the coil physically, how would i calculate the physical resistance it generates cause of repelling magnetic fields?

My attempt(EDIT1):

d1=distance from the straight conductor to the near side of the coil

d2=distance from the straight conductor to the far side of the coil

B1=(μ0∗I)/(2∗π∗d1)

B2=(μ0∗I)/(2∗π∗d2)

Bavg=(B1+B2)/2

I would reduce it by 30% because of radial nature of the magnetic field which weakens linearily with distance and the coil which overlaps with the magnetic field so:

Bavg=0,7*(B1+B2)/2

and finally

Ep=A*N*B*2*π*f

Erms=Ep/sqrt(2)

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