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 $B',$ at radial distances $\frac{a}{2}$ and $2a$ respectively, from the axis of the wire is
NEET 2016, Medium
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Magnetic field at a point inside the wire at distance $r\left(=\frac{a}{2}\right)$ from the axis of wire is
$B=\frac{\mu_{0} I}{2 \pi a^{2}} r=\frac{\mu_{0} I}{2 \pi a^{2}} \times \frac{a}{2}=\frac{\mu_{0} I}{4 \pi a}$
Magnetic field at a point outside the wire at distance $r(=2 a)$ from the axis of wire is
$B^{\prime}=\frac{\mu_{0} I}{2 \pi r}=\frac{\mu_{0} I}{2 \pi} \times \frac{1}{2 a}=\frac{\mu_{0} I}{4 \pi a} \quad \therefore \frac{B}{B'}=1$
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