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

Options

A.
B.
C.
D.

Answer

D

Explanation

Case-I `xltR/2`
`|B|=0`
CaseII
`intvecB.dvecl=mu_(0)l`
`|B|2pix=mu_(0)[pix^(2)-pi(R/2)^(2)]J`
`|B|=(mu_(0)J)/(2x)(x^(2)-R^(2)/4)`
Case-III
`intvecB.dvecl=mu_(0)l`
`|B|2pix=mu_(0)[piR^(2)-pi(R/2)^(2)]J`
`|B|=(mu_(0)J)/(2x)3/2R^(2)`
`|B|=(3mu_(0)JR)^(2)/(8x)` So
`|B|`