Question

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 $\frac{a}{3}$ and $2a$, respectively from the axis of the wire is :

• A. 3/2
• B. 2
• C. 2/3
• D. 1/2

Answer 1

Answer: (C)

Let current density be $J$.
$\therefore$ Applying Ampere's law.
$\oint \vec{B}.d\vec{\ell }={\mu }_{0}i\Rightarrow B_{A}2\pi \frac{a}{3}{\mu }_{0}J\pi {\left(\frac{a}{3}\right)}^2$
$\therefore B_A=\frac{{\mu }_{0}Ja}{6}$
Similarly, $B_B=\frac{{\mu }_{0}Ja}{4}$
$\therefore \frac{B_A}{B_B}=\frac{{\mu }_{0}Ja\times 4}{{\mu }_{0}J6a}=\frac{2}{3}$