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

beljuA 2021-03-30 Answered
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 2.0×108 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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Expert Answer

timbalemX
Answered 2021-04-01 Author has 108 answers
Jeffrey Jordon
Answered 2021-09-29 Author has 2027 answers

a) E=ρlA

b) dEdt=ddt(ρlA)

=ρAdldt

=2.0×108 Ohm2.1×106 m2(4000 A/s)

=38 V/m×s

c) The dispacement current in the material is jp=ϵ0dEdt=ϵ0(38 V/s2m)=3.4×1010 A/m2

d) ip=jpA=(3.4×1010 A/m2)(2,1×106m2)=7.14×1016 A

Bp=μ0Ip2πr=μ0(7.14×1016A)2π(0.060m)=2.38×1021T So this is a neglisible contribution

Bc=μ0Ic2πr=μ02π(16 A)(0.060m)=5.33×105T

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