A long straight wire of radius a carries a steady current $I$. The current is uniformly distributed

Question

A long straight wire of radius a carries a steady current $I$. The current is uniformly distributed over its cross-section. The ratio of the magnetic fields $B$\ and $B^{\prime}$, at radial distances $a / 2$ and $2 a$ respectively, from the axis of the wire is\

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(a) : Magnetic field at a point inside the wire at distance $r\left(=\frac{a}{2}ight)$ from the axis of wire is $$ B=\frac{\mu_{0} I}{2 \pi a^{2}} r=\frac{\mu_{0} I}{2 \pi a^{2}} 	imes \frac{a}{2}=\frac{\mu_{0} I}{4 \pi a} $$ Magnetic field at a point outside the wire at a distance $r(=2 a)$ from the axis of wire is $$ B^{\prime}=\frac{\mu_{0} I}{2 \pi r}=\frac{\mu_{0} I}{2 \pi} 	imes \frac{1}{2 a}=\frac{\mu_{0} I}{4 \pi a} \quad 	herefore \frac{B}{B^{\prime}}=1 $$