Match List-I with List-II regarding the variation of magnetic field ( B ) with distance ( r ) from the axis of a long current-carrying conductor. List-I List-II (A) Inside a long solid wire (I) B r (B) Outside a long solid wire (II) B 1 r (C) Inside a long thin hollow pipe (III) B = 0 (D) Outside a long thin hollow pipe (IV) B 1 r^2 Choose the correct answer from the options given below:

Step-by-step solution

According to Ampere's circuital law, B d l = ₀ I_ enclosed . For a long solid wire of radius R carrying steady current I : Inside the wire ( r Outside the wire ( r R ), the enclosed current is I , which gives B = ₀ I 2 r . Thus, B 1 r . For a long thin hollow pipe carrying steady current I : Inside the pipe, the enclosed current is zero, so B = 0 . Outside the pipe, the enclosed current is I , which gives B = ₀ I 2 r . Thus, B 1 r . Therefore, the correct matching is (A)-(I), (B)-(II), (C)-(III), (D)-(II). Answer: