Question

A long straight wire of radius $'a'$ caries a steady current $i$. The current across its cross section. The ratio of the magnetic field at $\frac{a}{2}$ and $2a$ is

• A. $\frac{1}{4}$
• B. $4$
• C. $1$
• D. $\frac{1}{2}$

Answer 1

Answer: (C)

$1$

Answer 2

$B2\pi \frac{a}{2}=\mu_{0} \frac{i}{\pi a^{2}}\left(\frac{\pi a^{2}}{4}\right)$ $B_{1}=\frac{\mu_{0}i}{4\,\pi a}\,...\left(i\right)$ $B_{2}2\pi\left(2a\right)=\mu_{0}i$ $B_{2}=\frac{\mu_{0}i}{4\,\pi a}\,...\left(ii\right)$ $\frac{B_{1}}{B_{2}}=1$