Curves in the graph shown, give as function of radial distance r, the magnitude B of the magnetic field 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 labels.
(i) Which wire has the greatest radius?
Text Solution
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Ans.
(i)
Sol. Inside the cylinder
B.2 π r = µ 0 
π r 2 B = 
. r ...............(1)
outside the cylinder
B.2 π r = µ 0 I
∴ B = 
................(2)
inside cylinder B ∝ r and outside B ∝ 
so from surface nature of magnetic field changes Hence it is clear from the graph that wire 'c' has greatest radius.
(ii)
Sol. magnitude of magnetic field is maximum at the surface of wire 'a'
(iii)
Sol. inside the wire
B(r) = 
. 
.r
= 
. 
i.e. slope ∝ 
∝ current density
It can be seen that slope of curve for wire 'a' is greater than wire 'c'.
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