1.

A long straight cable of length l is placed symmetrically along z-axis and has radius a(ltlt l). The cable consists of a thin wire and a co- axial conducting tube. An alternating current I(t) = I_(0) " sin " (2pi vt).Flows down the central thin wire and returns along theco-axial conducting tube. the induced electric at a distance s from thewire inside the cable is E(s ,t) =mu_(0) I_(0) v " cos "(2pivt) In ((s)/(a)) hatk. (i) Calculate the displacement current density inside the cable. (ii) Integrate the displacement current density across the cross- section of the cable to find the total displacement current I^(d). (iii) compare theconduction current I_(0) with thedisplacement current I_(0)^(d).

Answer»

`(2pi)/(LAMDA^(2))I_(0)LN((a)/(s))sin(2pi upsilont)hat(k)`
`(1)/(lamda^(2))I_(0)ln((a)/(s))sin(2pi upsilont)hat(k)`
`(pi)/(lamda^(2))I_(0)ln((a)/(s))sin(2pi upsilon t)hat(k)`
Zero

Solution :Displacement current density, `vecJ_(d)=epsilon_(0)(dvecE)/(DT)`
`=epsilon_(0)mu_(0)I_(0)upsilon(del)/(delt)upsiloncos(2piupsilont)ln.((s)/(a))hatk`
`=(1)/(c^(2))I_(0)2piupsilon^(2)(-sin(2piupsilont))ln.((s)/(a))hatk`
`=((upsilon)/(c))^(2)2piI_(0)sin(2piupsilont)ln.((a)/(s))hatk=(2pi)/(lambda^(2))I_(0)ln.((a)/(s))sin(2piupsilont)hatk`


Discussion

No Comment Found

Related InterviewSolutions