EMF/Eddy Currents Induced in a Hollow Cylindrical Conductor

[cyborg6060]

I'm attempting to figure out the total current induced in a hollow metal tube as a result of the EMF due to a constantly varying magnetic flux through its cross-section.

Faraday's law of induction states that for an infinitely thin loop of wire in such varying magnetic flux has induced EMF $ε=-\frac{d\phi}{dt}$.

For a cylindrical solenoid composed of N circular windings of wire, the EMF induced is $ε=-N\frac{d\phi}{dt}$.

My question is: How would one go about calculating the EMF induced in a continuous metal tube? Or, if possible by any other means, the how would one find total current induced around the tube?

 

[Vailanor]

The answer to this question is complicated and depends on a number of factors, as there is no single formula for calculating the total current induced in a continuous metal tube. The EMF induced can be calculated using Ampere's law, which states that the line integral of the magnetic field around a closed path is equal to the total current enclosed by the path multiplied by the permeability of the medium. This law can be used to calculate the EMF induced in a continuous metal tube by taking the line integral of the magnetic field around the tube and multiplying it by the permeability of the medium. Other factors that need to be taken into consideration include the geometry of the tube, the permeability of the medium, and the rate at which the magnetic flux is changing.