A long straight solenoid has `n` turns per unit length. An alternating current `I = I_(m) sin omega t` flows throught it. Find the displacement current density as a function of the distnace `r` from the solenoid equals `R`.

Explanation

Inside the solenoid, there is a magnetic field,
`B = mu_(0) n I_(m) sin omega t`.
since this varies in time there is an associated electric field. This is obtained by using,
`oint_(C) vec(E).d vec(r) = - (d)/(dt) int_(S) vec(B). D vec(S)`
For `r lt R, 2pi r E = - dotB. pi r^(2)`, or, `E = -(dotB r)/(2)`
For`r gt R, E = =- (dotB R^(2))/(2r)`
The associated displacement current density is
`j_(4) = epsilon_(0) (del E)/(del t) = [{:(-epsilon_(0) ddotB r//2),(-epsilon_(0) ddotB R^(2)//2r):}`
The answer given in the book, is dimensionally incorrect without the factor `epsilon_(0)`