# 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

A long, straight, copper wire with a circular cross-sectional area of $2.1m{m}^{2}$ 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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###### Not exactly what you’re looking for?
Jeffrey Jordon

a) $E=\frac{\rho l}{A}$

b) $\frac{dE}{dt}=\frac{d}{dt}\left(\frac{\rho l}{A}\right)$

$=\frac{\rho }{A}\frac{dl}{dt}$

c) The dispacement current in the material is

d)

$⇒{B}_{p}=\frac{{\mu }_{0}{I}_{p}}{2\pi r}=\frac{{\mu }_{0}\left(7.14×{10}^{-16}A\right)}{2\pi \left(0.060m\right)}=2.38×{10}^{-21}T$ So this is a neglisible contribution