Question

A long straight wire of radius $R$ carries a steady current $I$ . The current is uniformly distributed across its cross-section. The ratio of magnetic field at $R/2$ and $2R$ is

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

Answer 1

Answer: (D)

The magnetic field inside the current carrying wire
$B$ at $\frac{R}{2}$ distance,
$B_{R/2}=\frac{{\mu }_{0}i}{2\pi R^2}\times \frac{R}{2}=\frac{{\mu }_{0}i}{4\pi R}$
At distance, $2R$
$B_{2R}=\frac{{\mu }_{0}i}{2\pi \left(2R\right)}=\frac{{\mu }_{0}i}{4\pi R}$
$\therefore \frac{B_{R/2}}{B_{2R}}=1:1$