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In: Physics

A long cylindrical wire made of a magnetic metal with relative permeability has a uniform current...

A long cylindrical wire made of a magnetic metal with relative permeability has a uniform current density J flowing along its length. An insulated wire runs along the axis of the cylinder and carries a current I. Find the magnetic field, magnetic induction, magnetization, and bound currents in the magnetic material.

Solutions

Expert Solution

Answer :

Given data :

Length of cylinder = L

Current density = J

Relative permeability =

According to Ampere's circuital law,

Integral of magnetic field density with respect to a gaussian sirface is directly proportional to Current enclosed in that surface.

So, in case of cylinder for B Inside the cylinder,

so inside the cylinder, as Current I = multiplication of current density and Area of cross section.

So  

So  Magnetic induction

In a medium Magnetic induction and magnetic field are related as,

So Magnetic field

Similarly Relation between Magnetic induction B and Magnetization is,

Putting the values of B and H in above equation, we get

Magnetization M =

The formula of Bound current is

So,

In magnetic material, Bound Current

genius_generous answered 1 year ago
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