A uniform current is flowing along the length of an infinite, straight, thin, hollow cylinder of radius 'R'. The magnetic field 'B' produced at a perpendicular distance 'd' from the axis of the cylinder is plotted in a graph. Which of the following figure looks like the plot?

Options

A.
B.
C.
D.

Answer

C

Explanation

For `d gt R` By symmetry, the Amperian loop is a circle. `oint vec(B). d vec(l)= oint B dl cos theta= mu_(0)I`
`:. mu_(0)I= oint vec(B).d vec(l)= oint Bdl = B underset(0)overset(2pi r)int dl [ :. theta= 0^(@)]`
`=B 2pi R` ( `:.`B= constant)
`:.` Using Ampere.s law, `B 2pi R= mu_(0)I`
`:. B= (mu_(0)I)/(2pi R)`
For `d lt R [ :. theta= 0^(@)]`
`:. B 2pi r= mu I_("in") or B= (mu I_("in"))/(2pi r) rArr B=0 ( :. I_("in")= 0)`