A cylindrical conductor of radius `R` is carrying constant current. The plot of the magnitude of the magnetic field, `B` with the distance, `d` from the centre of the conductor , is correctly represented by the figure:

Options

A.
B.
C.
D.

Answer

D

Explanation

From ampere circuital law-
`oint B.dl = mu_(0) I. " " [because I.= (I)/(pi R^(2)) xx pi r^(2)]`
Magnetic field inside the conductor
`B* 2pi r = mu_(0) "" (1)/(pi R^(2)) xx pi r^(2) impliesB = (mu_(0) I)/(2pi R^(2)) ` (inside)
`B_("inside") prop r`
Magnetic field outside the conductor - `ointB .dl = mu_(0) I`
`B* 2pi r = mu_(0) I implies B = (mu_(0) I)/(2pi r)`
`B_("outside") prop (1)/( r)`