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 :
A.
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 wire (r a) The current enclosed by an Amperian loop of radius r is the total current I. Applying Ampere's law: B(2 r) = _0 I B = _0 I 2 r Thus, B 1 r . The graph is a rectangular hyperbola. At the surface (r = a), the magnetic field is maximum: B = _0 I 2 a . The plot that correctly represents this variation shows a linear increase from the origin up to r = a, followed by a 1/r decrease for r > a. This matches the first graph. Answer:
Related: Physics — Magnetic Effects of Current · All PYQ Banks