A thick current carrying cable of radius R carries current I uniformly distributed across its cross-section. The variation of magnetic field B ( r ) due to the cable with the distance r from the axis of the cable is represented by:

Step-by-step solution

For inside part J = I π R 2 ∫ B → · d l → = μ 0   I i n c l o s e d         … i B   2 π r = μ 0 I π R 2 × π r 2 B   2 π r = μ 0 I r 2 R 2 B ∝ r For outside part ∫ B → · d l → = μ 0 I i n c l o s e d B ( 2 π r ) = μ 0 I ∴     B ∝ 1 r