Modelling a metal detector using eddy currents from Non-Destructive Testing

AI Thread Summary
The discussion focuses on modeling a metal detector using eddy currents for an internship project. The system involves a coil energized by an oscillator to generate a magnetic field, with detection based on changes in coil impedance. The magnetic field produced by the coil is described using Biot-Savart law, while induced voltage in the target is determined by Faraday's law. The user seeks to find the expression for the magnetic field induced by eddy currents, specifically questioning if it takes a form like Bind = B0eiwt. The request for assistance emphasizes the need for results to initiate simulations and includes links to relevant resources for further clarification.
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Homework Statement
Modelling a metal detector
Relevant Equations
∇×E=− ∂/∂t(∇×B)
∇×B=μ0ε0∂/∂t(E)
I'm trying to model a metal detector for my internship project.
The system consist of one coil energised with an oscillator to create a magnetic field. The principle of the detection is by measuring the change in the coil impedance.
with biot et savart law the magnetic field create by the coil is expressed
1715018724594.png

where
Bem(r) : the magnetic field create by the coil
N : number of loops
Iem : current flowing through the coil
Rem : radius of the coil
r : distance from a given point in space to a point on the perimeter of the coil

The induced voltage in the target is given with faraday's law
1715019133773.png






where phi is the magnetic flux
I'm trying to find the expression of Bind the magnetic induced by eddy currents.
This is my results :
1715021033350.png

Now I've got a problem. Does Bind have a particular form? something like Bind = B0eiwt? or anything else? I need these results to start simulations so any help is welcomed thank you very much
 
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