Magnetic field due to currentHard

Question

A long straight wire of radius a carries a steady current i. The current is uniformly distributed across its cross section. The ratio of the magnetic field at a/2 and 2a is

Options

A.1/2
B.1/4
C.4
D.1

Solution

       
Here, current is uniformly distributed across the cross-section of the wire, therefore current enclosed in the amperean
path formed at a distance r1
= × I, where Iis total current
∴   Magnetic field at
P1(B1) =

Now, magnetic field at point P2′
(B) =
∴ Required Ratio =

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