Question

An infinitely long hollow conducting cylinder with inner radius `(r )/(2)` and outer radius `R` carries a uniform current ra density along its length . The magnitude of the magnetic field , ` | vec(B)|` as a function of the radial distance `r` from the axis is best represented by
A.
B.
C.
D.

Answer 1

Correct Answer - D
(d) Case-I: `x gt R/2`
`|B|=0`

Case-II: `R/2lexleR`
`intvecB.vec(dl)=mu_0I`
`|B|2pix=mu_0[pix^2-pi(R/2)^2]J`
`|B|=(mu_0J)/(2x)(x^2-(R^2)/4)`
Case III: `xgeR`
`intvecB.vec(dl)=mu_0I`
`|B|2pix=mu_0[piR^2-pi(R/2)^2]J`
`|B|=(mu_0J)/(2x) 3/4 R^2`
`|B|=(3mu_0JR^2)/(8x)`
so