Question

A long cylindrical wire of radius R carries a current $i$ distributed uniformly over its cross section.Find the maximum magnetic field produced by this wire.

• A. $\frac{{\mu }_{0}il}{2\pi R}$
• B. $\frac{8{\mu }_{0}l}{\pi R}$
• C. $\frac{{\mu }_{0}l}{4\pi R}$
• D. $\frac{2{\mu }_{0}l}{\pi R}$

Answer 1

The correct option is A $\frac{{\mu }_{0}il}{2\pi R}$

Let the current $i$ is uniformly distributed throughout the wire.

$R$ is the radius of the cylindrical wire.

From Ampere's circuital law, $\varphi B\times dl=B\times 2\pi l$ (where $l$ is a small part of the ring)

For maximum magnetic field, $B={\mu }_0\frac{i{l}^2}{R}\times \frac{1}{2\pi l}=\frac{{\mu }_{o}il}{2\pi R}$