A cylindrical conductor of radius R is carrying a 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

Magnetic field due to long solid cylindrical conductor of radius R ,
(i) For `d lt R, I.= (Id^2)/(R^2)`
`int vecB.dvecl = mu_0 I. rArr B(2pid) = (mu_0Id^2)/(R^2) rArr B = (mu_0Id)/(2piR^2)`
`therefore B prop d`
(ii) For d = R, B = `mu_0 I//2 pi R` (maximum)
(iii) For `d gt R, B = mu_0 I//2pid rArr B prop 1//d`