Faraday induction in constant B field, with non-conduction wires

In summary, the conversation discusses a standard textbook problem involving a constant magnetic field and a conducting loop that increases in area at a constant rate. It is easy to calculate the induced EMF and the associated electric field magnitude and direction, as well as the current in the loop and the rate of dissipation. The question is raised about the scenario where the wire is a perfect insulator, and it is asked whether there will still be an induced EMF and polarization in the insulating material. It is noted that there will be no current and no induced magnetic field, which seems to contradict Maxwell's curl equations. The possibility of polarization in a dielectric material is also mentioned.
  • #1
FFXT
1
1
A standard textbook problem features a constant B field and a conducting loop that increases in area at constant rate.
It is easy to work out the induced EMF and the associated electric field magnitude and direction (CW or CCW). The magnitude of the E field
is E = B v where v is a velocity. The current in the loop is easy to work out and the rate of dissipation (I^2 R) compared with the external work/power needed to keep the loop area expanding at a constant rate.

My question is: What if the wire is actually a perfect insulator? Will there still be the same EMF and will that induce polarization in the dielectric
insulating material? There will be no current so, apparently, so no induced magnetic field thus no rate of change of magnetic field.
How is that consistent with the differential form of Maxwell's curl equations?
 
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  • #2
When the wire is made larger the positive and negative charges are moved raadially and feel opposite tangential forces frrom Lorentz force. I would expect polarization in a polarizeable dielectric material
 
  • #3
If the "wire" is a dielectric you'll also have the said EMF, which will polarize the wire.
 

1. What is Faraday induction?

Faraday induction is the process of creating an electric current in a conductor by changing the magnetic field around it. This phenomenon was first discovered by Michael Faraday in the 19th century.

2. How does Faraday induction work?

Faraday induction occurs when a conductor, such as a wire, is moved through a magnetic field or when the magnetic field around the conductor changes. This movement or change in the magnetic field creates an electric current in the conductor.

3. What is a constant B field?

A constant B field is a magnetic field that does not change in strength or direction over time. In other words, the magnetic field has a constant magnitude and is not affected by external factors.

4. Can Faraday induction occur with non-conducting wires?

No, Faraday induction requires a conductor in order to create an electric current. Non-conducting wires, such as plastic or rubber, do not allow for the flow of electrons and therefore cannot undergo Faraday induction.

5. What are some practical applications of Faraday induction in constant B fields?

Faraday induction in constant B fields is used in various technologies, such as generators, transformers, and electric motors. It is also the principle behind wireless charging and induction cooktops.

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