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

Let `j:` current density
`r lt R/2, B=0`
`R/2ler le R, Bxx2pir=mu_(0)jpi(r^(2)-(R^(2))/4)`
`B=(mu_(0)j)/2(r-(R^(2))/(4r))`
`B` versus `r` Will be a curve
`r gt R, Bxx2pir=mu_(0)jpi(R^(2)-(R^(2))/4)`
`B=(mu_(0)j)/2. (3R^(2))/(4r), B prop 1//r`(rectangular hyperbola)