In: Physics
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.
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