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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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

2.1 m m^{2}

carries a current of 16 A. The resistivity of the material is

2.0 \times 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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timbalemX

Answered 2021-04-01 Author has 108 answers

I provide the solution below:

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Jeffrey Jordon

Answered 2021-09-29 Author has 2027 answers

a) $E = \frac{ρ l}{A}$

b) $\frac{d E}{d t} = \frac{d}{d t} (\frac{ρ l}{A})$

$= \frac{ρ}{A} \frac{d l}{d t}$

$= \frac{2.0 \times 10^{- 8} O h m}{2.1 \times 10^{- 6} m^{2}} (4000 A / s)$

$= 38 V / m \times s$

c) The dispacement current in the material is $j_{p} = ϵ_{0} \frac{d E}{d t} = ϵ_{0} (38 V / s^{2} m) = 3.4 \times 10^{- 10} A / m^{2}$

d) $i_{p} = j_{p} A = (3.4 \times 10^{- 10} A / m^{2}) (2, 1 \times 10^{- 6} m^{2}) = 7.14 \times 10^{- 16} A$

$\Rightarrow B_{p} = \frac{μ_{0} I_{p}}{2 π r} = \frac{μ_{0} (7.14 \times 10^{- 16} A)}{2 π (0.060 m)} = 2.38 \times 10^{- 21} T$ So this is a neglisible contribution

$B_{c} = \frac{μ_{0} I_{c}}{2 π r} = \frac{μ_{0}}{2 π} \frac{(16 A)}{(0.060 m)} = 5.33 \times 10^{- 5} T$

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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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