Question bank/JEE Main/Physics

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

A$\frac{1}{2}$B2C$\frac{3}{2}$D$\frac{2}{3}$

Show answer and solution▾

$B_{A} = \frac{\mu_{0}ir}{2\pi a^{2}} = \frac{\mu_{0}i\frac{a}{3}}{2\pi a^{2}} = \frac{\mu_{0}i}{\pi a^{2}}\frac{a}{6} = \frac{\mu_{0}i}{6\pi a}$
$B_{B} = \frac{\mu_{0}i}{2\pi(2a)}$
$\frac{B_{A}}{B_{B}} = \frac{4}{6} = \frac{2}{3}$

Source: Grass-G / P-19 Physics paper 28 Nov Fourth.docx