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

Question

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

Accepted Answer

Inside the wire ($r < R$), the magnetic field $B = \frac{\mu_0 I r}{2 \pi R^2}$, which is linearly increasing with $r$. Outside the wire ($r > R$), the magnetic field $B = \frac{\mu_0 I}{2 \pi r}$, which is proportional to $\frac{1}{r}$.

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