A long straight wire with a circular cross-section having radius R , is carrying a steady current I . The current I is uniformly distributed across this cross-section. Then the variation of magnetic field due to current I with distance r r R from its centre will be

Question

A long straight wire with a circular cross-section having radius R , is carrying a steady current I . The current I is uniformly distributed across this cross-section. Then the variation of magnetic field due to current I with distance r r R from its centre will be, B ∝ r, B ∝ 1 r, B ∝ r 2, B ∝ 1 r 2

MARKS App · Accepted Answer

Using Ampere's law and noting that the steady current is uniformly distributed over the cross-section of the cylindrical wire. B = μ 0 I r 2 π R 2 , r ≤ R μ 0 I 2 π r , r > R Thus, magnetic field B ∝ r from the centre for r R .

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