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A long straight wire of radius ' $a$ ' caries a steady current $\mathrm{i}$. The current is uniformly distributed across its cross section. The ratio of the magnetic field at $\frac{a}{2}$ and $2 a$ is
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$\mathrm{B} 2 \pi \frac{\mathrm{a}}{2}=\mu_0 \frac{\mathrm{i}}{\pi \mathrm{a}^2}\left(\frac{\pi \mathrm{a}^2}{4}\right)$
$\mathrm{B}_1=\frac{\mu_0 \mathrm{i}}{4 \pi \mathrm{a}} \quad \ldots$ (i)
$\mathrm{B}_2 2 \pi(2 \mathrm{a})=\mu_0 \mathrm{i}$
$\mathrm{B}_2=\frac{\mu_0 \mathrm{i}}{4 \pi \mathrm{a}} \quad \dots (ii)$
$\frac{\mathrm{B}_1}{\mathrm{~B}_2}=1$
$\mathrm{B}_1=\frac{\mu_0 \mathrm{i}}{4 \pi \mathrm{a}} \quad \ldots$ (i)
$\mathrm{B}_2 2 \pi(2 \mathrm{a})=\mu_0 \mathrm{i}$
$\mathrm{B}_2=\frac{\mu_0 \mathrm{i}}{4 \pi \mathrm{a}} \quad \dots (ii)$
$\frac{\mathrm{B}_1}{\mathrm{~B}_2}=1$
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