Question

A long straight wire of radius `a' caries a steady current i. The current is uniformly distributed 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

The correct option is C 1

$B_2\pi \frac{a}{2}={\mu }_0\frac{i}{\pi a^2}\left(\frac{\pi a^2}{4}\right)B_1=\frac{{\mu }_{0}i}{4\pi a}\dots \dots \left(i\right)B_{2}2\pi \left(2a\right)={\mu }_{0}i{B}_2=\frac{{\mu }_{0}i}{4\pi a}\dots \dots \left(ii\right)\frac{B_1}{B_2}=1$