Curves in the graph shown give , as functions of radial distance r (from the axis), the magnitude B of the magnetic field (due to individual wire) inside and outside four long wires a ,b,c and d, carrying currents that are uniformly distributed across the cross sections of the wires. Overlapping portions of the plots are indicated by double lables . All curves start from the origin.

(i). Which wire has the greatest radius ?
(A) a
(B) b
(C ) c
(D) d
(ii) Which wire has the greatest magnitude of the magnetic field on the surface ?
(A) a
(B) b
(C ) c
(D) d
(iii) The current density in wire a is
(A) greater than in wire c.
(B) less than in wire c.
(C ) equal to that in wire c.
(D) not comparable to that of in wire c due to lack of information.

Explanation

Inside the cylinder
`B.2pir=mu_(0).(I)/(piR^(2))pir^(2)`
`B=(mu_(0)I)/(2piR^(2))r` …… (1)
outside the cylinder
`B.2pir=mu_(0)I`
`thereforeB=(mu_(0)I)/(2pir)` ..... (2)

Inside cylinder B `alpha` r and outside `Balpha(1)/(r)`
So at the surface nature of magnetic field changes. Hence clear from geaph, wire 'c' has greatest radius.
Magnitude of magnetic field is maximum at the surface of wire 'a'
Inside the wire
`B(r)=(mu_(0))/(2pi).(I)/(R^(2)).r=(muJr)/(2)`
`(dB)/(Dr)=(mu_(0)J)/(2)` i.e slope `propJ`
`prop` current density
It can be seen that slope of curve for wire a is greater than wire C.