An alternating current I $=$sin$()$ flows down a long straight wire, and returns along a

coaxial conducting tube of radius a$.$ Assuming that the induced electric field goes to zero as s $$ and E$($s$,$ t$)$

can be determined as

$(,)=$

$2$ cos$()$ ln $$

$$

$1)$ Find the displacement current density Jd$.$

$2)$ Find the total displacement current Id$.$

$3)$Find the ratio Id $/$ I.

$4)$ Assuming the outer cylinder $=4$ mm in diameter, Id $/$ I $=2\%,$ what would the frequency be in this scenario?

$5)$ Explain why Faraday never discovered displacement currents.