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An infinitely long hollow conducting cyl...

An infinitely long hollow conducting cylinder with inner radius `(R)/(2)` and outer radius `R` carries a uniform current 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

Text Solution

Verified by Experts

The correct Answer is:
D

`r="distance of a point centre"`
For `rleR/2`
using Ampere's circuital law,
`ointB.dI=mu_0i_("net")`
`Bl=mu_0(I_("in"))`
or `B(2pir)=mu_0(I_("in"))`
or `B=mu_0/(2pi) I_("in")/r`
or `I_("in")=0`
`since, B=0`
`:. I_("in")=[pir^2-pi(R/2)^2]sigma`
Here `sigma`=current per unit area
Substituting in eqn i we have
`B=(mu)/(2pi)([pir^2-piR^2/4]sigma)/r`
`=(mu_0sigma)/(2r)(r^2-R^2/4)`
`At r=R/2, B=0`
`At r=R, B=(3mu_0sigmaR)/8`
`for rgeR I_(in)=I_(Total)=I(say)`
Therefoe substituting in Eq. i we have
`B=mu_0/(2pi).I/r or Bprop 1/r`
`:.` the current graph is d.
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