A current with a constant current density of Js=1π (A/m2 ) in the +z direction from the radius wire, and from the infinitely long cylindrical shell with inner radius b=3m and outer radius c=4m, constant I=4 Amperes homogeneously distributed in the cross section in the −z direction current is flowing. Accordingly, using the Ampere formula, calculate the magnetic field in regions rc.
Ampere Circuital Law
Ampere's Law states that "for any closed loop path, the sum of the length elements times the magnetic field in the direction of the length element is equal to the permeability times the electric current enclosed in the loop.”
Current Density
To design the electrical and electronic system, the current density is an important factor. The designer current level is the factor on which the circuit performance depends and with the help of the dimensions of the conducting current the current density is then determined. For instance, despite the lower current demanded by smaller devices as integrated circuits are reduced in size, there is a type of trend in achieving the higher device number in even smaller chip areas. The current density is increased in this region at higher frequencies because the conducting region in a wire becomes confined and this is known as the skin effect. The consequences increase as the current densities become higher.
A current with a constant current density of Js=1π (A/m2 ) in the +z direction from the radius wire, and from the infinitely long cylindrical shell with inner radius b=3m and outer radius c=4m, constant I=4 Amperes homogeneously distributed in the cross section in the −z direction current is flowing. Accordingly, using the Ampere formula, calculate the magnetic field in regions r<a,a<r<b,b<r<c and r>c.
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