Refer to Prob. 7.16, to which the correct answer was (a) Find the displacement...

Refer to Prob. 7.16, to which the correct answer was

(a) Find the displacement current density J_d .

(b) Integrate it to get the total displacement current,

(c) Compare I_d and I . (What’s their ratio?) If the outer cylinder were, say, 2 mm in diameter, how high would the frequency have to be, for I_d to be 1% of I? [This problem is designed to indicate why Faraday never discovered displacement currents, and why it is ordinarily safe to ignore them unless the frequency is extremely high.]

Reference problem 7.16

An alternating current I = I₀ cos (ωt) flows down a long straight wire, and returns along a coaxial conducting tube of radius a.

(a) In what direction does the induced electric field point (radial, circumferential, or longitudinal)?

(b) Assuming that the field goes to zero as s →∞, find E(s, t).¹⁵