From Ampere's circuital law for a long straight wire of circular cross-section carrying a steady current,…

From Ampere's circuital law for a long straight wire of circular cross-section carrying a steady current, the variation of magnetic field in the inside and outside region of the wire is
  1. a linearly increasing function of distance upto the boundary of the wire and then linearly decreasing for the outside region.
  2. a linearly increasing function of distance r upto the boundary of the wire and then decreasing one with  1r dependence for the outside region.
  3. a linearly decreasing function of distance upto the boundary of the wire and then a linearly increasing one for the outside region
  4. uniform and remains constant for both the regions.

Solution

If the current density in the wire is J then

For r<R

∮B→·dl→=μ0i

⇒  B2πr=μ0Jπr2

⇒  B=μ0J2r

⇒B∝r

For r>R

∮B→·dl→=μ0i→

⇒ B2πr=μ0πR2J

⇒ B=μ0R2J2r

⇒B∝1r

Asked in: NEET 2022 (Phase 1)

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