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

• Sh_lm
Sh_lm
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

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

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 :

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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