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Curves in the graph shown in Fig. give magnetic field as functions of radial distance ‘r’, the magnitude of 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. Over lapping portions of the plots are indicated by the double labels. (All graphs pass through origin)

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the wire ‘c’ has the greatest radius

the current density in wire ‘a’ is greater than that in the wire ‘c’

the wire that has the greatest magnitude of the magnetic field on the surface is ‘a’

the wire ‘a’ has the greatest radius

answer is A, B, C.

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Detailed Solution

Inside the wire

B (r) = \frac{μ_{0}}{2 π} \frac{I}{R^{2}} r \Rightarrow \frac{d B}{d r} = \frac{μ_{0}}{2 π} \frac{I}{R^{2}}

Slope $\propto \frac{1}{π R^{2}} \propto$ current density

It can be seen that slope of curve for wire ‘a’ is greater than wire ‘c’

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