Adding a Phase Element to Biot Savart Law

  • Thread starter lechko
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In summary, the conversation discusses adding a phase element to the Biot Savart law in order to make it applicable to various frequencies. The idea is to use the magnetic potential function, as demonstrated by Laplace, to derive the equation for magnetic field. However, the question remains on how to incorporate the phase element. The suggestion is to multiply the current flux by { exp(-jkr) } and then apply Faraday's Law for changing magnetic fields. Additionally, there is mention of using the Fourier or Laplace transform to solve the problem in the frequency domain.
  • #1
lechko
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Hi everyone, just got something new to do and got no idea where to start.
I'm trying to add a phase element to Biot Savart law (thus turning it from a static law to something that will apply to various freq.) to do that, I'm reading up on how the law was proved.
As far as i can understand, it all started from Laplace, using the magnetic potential function, you get the equation for magnetic field and so on... the question is how do i add the phase element in? is it as simple as multiplying J (current flux) by { exp(-jkr) } and going on with it to getting same as Biot Savart but with the added part?

I'm out of ideas here, so any help will be great. :confused:
 
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  • #2
Biot-Savart is an experimental law (But I think there's a derivation of it from maxwell's equations and relativity in the book "Principles of Electrodynamics" by Melvin Schwartz.) When you say static, I assume you mean magneostatic, since the law applies in the presence of a non-static electric field (which is manifested as a magnetic field without taking Lorentz into account.) I'm still not too clear what you are trying to do with it, but whenever you have a changing magnetic field, you will have to take into account Faraday's Law somehow.
 
  • #3
lechko said:
Hi everyone, just got something new to do and got no idea where to start.
I'm trying to add a phase element to Biot Savart law (thus turning it from a static law to something that will apply to various freq.)
I'm out of ideas here, so any help will be great. :confused:

I'm not sure of the details of what you're trying to do, but it seems to me that all you really want to do is to take the Fourier or laplace transform to take the problem out of the time domain into the frequency domain.
 

1. What is the Biot Savart Law?

The Biot Savart Law is a fundamental law in electromagnetism that describes the magnetic field produced by a current-carrying wire. It states that the magnetic field at a point in space is directly proportional to the current, the length of the wire, and the sine of the angle between the wire and the point.

2. How can a phase element be added to the Biot Savart Law?

A phase element can be added to the Biot Savart Law by incorporating the concept of phase difference between the current and the magnetic field. This can be done by introducing a time-varying term, such as the angular frequency, into the equation.

3. What is the significance of adding a phase element to the Biot Savart Law?

Adding a phase element to the Biot Savart Law allows for the consideration of time-varying current and magnetic fields, which is necessary for studying electromagnetic phenomena in many real-world scenarios. It also allows for a more accurate description of the relationship between current and magnetic field.

4. How does the addition of a phase element affect the Biot Savart Law equation?

The addition of a phase element changes the Biot Savart Law equation from a static relationship between current and magnetic field to a dynamic one. The equation will now include a term representing the phase difference between the two variables, making it more complex but also more comprehensive.

5. What are some examples of applications of the Biot Savart Law with a phase element?

The Biot Savart Law with a phase element has many practical applications, including the study of electromagnetic induction, the design of electric motors and generators, and the analysis of electromagnetic waves and communication systems. It is also used in medical imaging techniques, such as magnetic resonance imaging (MRI), which rely on time-varying magnetic fields to produce images of the body's tissues.

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