Chapter 31, Problem 60GP

Imagine that a steady current I flows in a straight cylindrical wire of radius R₀ and resistivity ρ. (a) If the current is then changed at a rate dI/dt, show that a displacement current I_D exists in the wire of magnitude ε₀ρ(dI/dt). (b) If the current in a copper wire is changed at the rate of 1.0 A/ms, determine the magnitude of I_D. (c) Determine the magnitude of the magnetic field B_D (T) created by I_D at the surface of a copper wire with R₀ = 1.0 mm. Compare (as a ratio) B_D with the field created at the surface of the wire by a steady current of 1.0 A.