A long straight cable of length l is placed symmetrically along z - axis and has radius `a(lt lt l)`. The cable consists of a thin wire and a co-axial conducting tube. An alternating current thin wire and returns along the coaxial conducting tube. The induced electric field at a distance s from the wire inside the cable is `vec(E )(s, t)=mu_(0)I_(0)v cos (2pi vt) ln ((s)/(a))hat(k)`
Compare the conduction current `I_(0)` with the displacement current `I_(0)^(d)`.

Explanation

Displacement current,
`I_(d)=(a)/(2)((pi a)/(lambda))^(2)I_(0)sin(2pi vt)=I_(0)^(d)sin(2pi vt)`
so `I_(0)^(d)=(a)/(2)((pi a)/(lambda))^(2)I_(0)`
`=((a pi )/(lambda))^(2)I_(0)xx ((a)/(2))`
`therefore (I_(0)^(d))/(I_(0))=(((a pi)/(lambda))^(2)I_(0)xx ((a)/(2)))/(I_(0))`
`=(a)/(2)((a pi)/(lambda))^(2)`
`=(a^(3)pi^(2))/(2 lambda^(2))`
Hence required ratio `(I_(0)^(d))/(I_(0))=(a^(3)pi^(2))/(2lambda^(2))`