The figure given below shows a long straight solid wire of circular cross-section of radius ' a ' carrying steady current I . The current I is uniformly distributed across its cross-section. The plot which correctly represents the variation of magnetic field ( B ) with distance ( r ) from the axis of the conductor in the region is :

Step-by-step solution

For a long straight solid wire of radius a carrying a steady current I uniformly distributed across its cross-section, we can find the magnetic field B at a distance r from the axis using Ampere's circuital law: B d l = ₀ I_ enclosed . Case 1: Inside the wire ( r The current enclosed by an Amperian loop of radius r is I_ enclosed = I ( r^2 a^2 ) = I r^2 a^2 . Applying Ampere's law: B(2 r) = ₀ (I r^2 a^2 ) B = ( ₀ I 2 a^2 ) r Thus, B r . The graph is a straight line passing through the origin. Case 2: Outside the wi