Question

Derive the magnetic field B inside and outside of an infinite thick wire with radius a=1. The wire carries a uniformly distributed current I=1A in the direction outwards the page.

Plot the magnetic flux density in the region -2<x<+2 and -2<y<+2 that is internal to the wire and external to the wire. The expected result should look like Fig.1

Fig.1

C:\Users\marcop\Documents\_Education_Teaching\PHYS325\FundamentalsElectromagneticsWithMatlab_course\Student Resources\Examples\JPEGs\example 03-04.jpg

using matlab

writeThe code typed

 The plots produced by the code

 The derivation or calculations required to write the code or to answer to the questions.

Answer 1

Flux density of magnetic field B around a current carrying wire is given by,

Hence flux density of magnetic field at a radial distance r,  

B(r) = ( I ) / ( 2 r) .............(1)

For magnetic field inside wire, current I is calculated as shown below

Let us consider the cross section of wire as shown in figure. Current I is uniformly distributed

Current passing through the cross section of radius r is obtained as

where j is current density across the area of cross section, j = I / (a²)

since a = 1, current passing through the cross section of radius r in side wire ( r < a ) is given by

I_r = (1/)r² = r²

Hence flux density of magnetic field inside wire ,

B(r) = [ (    ) / ( 2 r) ] r² = [ / (2) ] r , .......r a

Flux density of magnetic field outside the wire,  

B(r) = [ / (2 r) ]   ........ r > a

Plot of flux density of magnetic field is given below