An alternating current I Io cos(wt) flows down a long straight wire, and returns along a...

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An alternating current I Io cos(wt) flows down a long straight wire, and returns along a coaxial conducting tube of radius R. a) In what direction does the induced electric field point (radial, circumferential, or longitudinal) in the quasistatic regime? b) Assuming that the field goes to zero as p , find (p,t). c) Find the displacement current density Ja. d) Integrate it to get the total displacement current. e) Compare Ia and I. (What's their ratio? f) If the outer cylinder were, say, 2mm in diameter, how high would the frequency have to be, for Ia 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. An alternating current I Io cos(wt) flows down a long straight wire, and returns along a coaxial conducting tube of radius R. a) In what direction does the induced electric field point (radial, circumferential, or longitudinal) in the quasistatic regime? b) Assuming that the field goes to zero as p , find (p,t). c) Find the displacement current density Ja. d) Integrate it to get the total displacement current. e) Compare Ia and I. (What's their ratio? f) If the outer cylinder were, say, 2mm in diameter, how high would the frequency have to be, for Ia 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.

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