A long, straight, copper wire with a circular cross-sectional area of 2.1mm2 carries a current of 16 A. The resistivity of the material is 2.0×10−8 Om. a) What is the uniform electric field in the material? b) If the current is changing at the rate of 4000 A/s, at whatrate is the electric field in the material changing? c) What is the displacement current density in the material in part (b)? d) If the current is changing as in part (b), what is the magnitude of the magnetic field 6.0cm from the center of the wire? Note that both the conduction current and the displacement currentshould be included in the calculation of B. Is the contribution from the displacement current significant?

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A long, straight, copper wire with a circular cross-sectional area of 2.1mm2 carries a current of 16 A. The resistivity of the material is 2.0×10−8 Om.  a) What is the uniform electric field in the material?  b) If the current is changing at the rate of 4000 A/s, at whatrate is the electric field in the material changing?  c) What is the displacement current density in the material in part (b)?  d) If the current is changing as in part (b), what is the magnitude of the magnetic field 6.0cm from the center of the wire? Note that both the conduction current and the displacement currentshould be included in the calculation of B. Is the contribution from the displacement current significant?

timbalemX · Accepted Answer

I provide the solution below:

Jeffrey Jordon · Accepted Answer

a) E=ρlA  b) dEdt=ddt(ρlA)  =ρAdldt  =2.0×10−8 Ohm2.1×10−6 m2(4000 A/s)  =38 V/m×s  c) The dispacement current in the material is jp=ϵ0dEdt=ϵ0(38 V/s2m)=3.4×10−10 A/m2  d) ip=jpA=(3.4×10−10 A/m2)(2,1×10−6m2)=7.14×10−16 A  ⇒Bp=μ0Ip2πr=μ0(7.14×10−16A)2π(0.060m)=2.38×10−21T So this is a neglisible contribution  Bc=μ0Ic2πr=μ02π(16 A)(0.060m)=5.33×10−5T

A long, straight, copper wire with a circular cross-sectional area of 2.1mm^2 carries a current of 16 A. The resistivity of the material is 2.0\times1

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