Question

13. A long, straight, solid metal wire of radius 2 mm carries a
current uniformly distributed over its circular cross-section.
The magnetic field induction at a distance 2 mm from its axis
is B. Then the magnetic field induction at distance 1 mm
from axis will be
(a) B
(b) B/2
(c)2B
(d) 4B​

Answer 1

Explanation:

Given A long, straight, solid metal wire of radius 2 mm carries a  current uniformly distributed over its circular cross-section.  The magnetic field induction at a distance 2 mm from its axis  is B. Then the magnetic field induction at distance 1 mm  from axis will be

We know that from Ampere’s circuital law we get

 ʃ B.ds = μoi

      So B. 2π r = μoJ r^2

      So μo i / π R^2 π r^2

       Now B α r

Therefore when r reduces to half, the magnetic field reduces to half. So we get 0.5 B or B/2.