Curves in the graph shown in Fig. give, as function of radius distance r, the magnitude B of the magnetic field inside and outside four long wire 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 labels.

which wire has the greatest magnitude of the magnetic field on the surface?

Options

A. a
B. b
C. c
D. d

Answer

A

Explanation

(a)
Inside the wire
`B(r) =(mu_0)/(2pi) I/(R^2) r implies (dB)/(dr)=(mu_0)/(2pi) I/(R^2)`
i.e., Slope `prop I/(piR^2)prop` current density
It can be seen that slope of curve for wire a is greater than
wire c.