Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): The magnetic field inside a solid cylindrical conductor carrying a steady uniform current increases linearly with the distance from its axis. Reason (R): The current enclosed by an Amperian loop of radius r ( r In the light of the above statements, choose the most appropriate answer from the option

Step-by-step solution

By Ampere's Law, B d l = ₀ I_ enclosed . For a solid cylindrical conductor of radius R carrying a steady uniform current I , the current density is J = I R^2 . For an Amperian loop of radius r ( r Applying Ampere's Law for this loop: B(2 r) = ₀ I ( r^2 R^2 ) B = ( ₀ I 2 R^2 ) r This shows that the magnetic field B is directly proportional to r , meaning it increases linearly with the distance from the axis. This makes the Assertion (A) correct. Since the r^2 dependence of the enclosed current is the exact mathemati