Question 10 of 276

A long, straight Wire of radius a carries a current distributed uniformly over its cross-section. The ratio of the magnetic fields due to the wire at distance $\dfrac{a}{3}$ and $2a$ , respectively from the axis of the wire is:

A$\dfrac{2}{3}$B$2$C$\dfrac{1}{2}$D$\dfrac{3}{2}$

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Answer: (A) $\dfrac{2}{3}$

${B}_{A}=\dfrac{{\mu }_{0}ir}{2\pi {a}^{2}}=\dfrac{{\mu }_{0}i\dfrac{a}{3}}{2\pi {a}^{2}}=\dfrac{{\mu }_{0}i}{\pi {a}^{2}}\dfrac{a}{6}=\dfrac{{\mu }_{0}i}{6\pi a}$
${B}_{B}=\dfrac{{\mu }_{0}i}{2\pi \left(2a\right)}$
$\dfrac{{B}_{A}}{{B}_{B}}=\dfrac{4}{6}=\dfrac{2}{3}$