Question

#5 Displacement Current in a wire. A long, straight, copper wire with a circular are of 1.5 mm2 carries a current of 3 A. The resistivity of the material is cross-sectional are of 1.5mm2crries a current of 3A. The resistivity of the material is 2.0 × 10-8 Ω·m. (a.) What is the uniform electric field in the material? (b) If the current is changing at the rate of 6.6 × 107 A/s, at what rate is the electric field in the material changing? (c.) What is the displacement current density in the material in part (b)? (Hint: Since is very close to 1, use ( =6.) (d.) If the current is changing as in part (b.), what is the magnitude of the magnetic field 6.0em from the center of the wire? Note that both conduction current and the displacement current should be included in the caleulation of B. (e.) Is the contribution from the displacement current significant?

A long, straight, copper wire with a circular cross-sectional are of 1.5mmm^2 carries a current of 3 A

.

Answer 1

a).

E = I x rho/ A

= 3 x 2 x 10^-8/ (1.5 x 10^-6)

= 0.04V/m

b).

dE/dt= rho x dI/dt / A

= 8.8 x 10⁵ V/m.s

c).

D= e₀E

= 8.8 x 10^-12 x 8.8 x 10⁵

= 7.744 x 10^-6 A/m²

d). Now,

id=(jd)A

id=(7.744E-6)*(1.5E-6)=11.6E-12

And generalized version of Amepre's law states

Line integral of B*dl=mu-0(ic+id)

ic=(dE/dt)*(A)*(e-0)=11.6E-12

So the Bc part is Bc=(ic/(2*pi*.06m))

= 3.08E-11

Bd= 7.96 (Use 3A as id for finding Bd)

e). not significant clear from from above.