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 f

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

TestHub · Accepted Answer

Using Ampere's law and noting that the steady current is uniformly distributed over the cross-section of the cylindrical wire.

$B = [\begin{matrix} \frac{μ_{0} I r}{2 π R^{2}}, r \leq R \\ \frac{μ_{0} I}{2 π r}, r > R \end{matrix}]$

Thus, magnetic field $B \propto r$ from the centre for $r < R$ .

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