A long straight wire of radius a carries a steady current I . the current is uniformly distributed over its cross-section. The ratio of the magnetic fields B and B' , at radial distances a 2 and 2 a respectively, from the axis of the wire is:

Step-by-step solution

I n s i d e t h e w i r e B y a m p e r e ′ s l a w ∫ B → . d l → = μ 0 i e n c l o s e d ∫ B . d l cos ⁡ 0 = μ 0 I π a 2 . π a 2 2 B ∫ d l = μ 0 I 4 B 2 π a 2 = μ 0 I 4 B = μ 0 I 4 π a Outside the wire, B ′ = μ 0 I 2 π r = μ 0 I 2 π 2 a = μ 0 I 4 π a So, B B ′ = 1 .