Question

A long straight' solid metal wire of radius 2mm caries current uniformly distributed over its circular cross section. The magnetic field induction at a distance 2mm from its axis is B . Then the maghetic field induction at a distance 1 mm from the axis will be

• A. B
• B. B/2
• C. 2B
• D. 3B

Answer 1

Answer: (B)

$B\int dl={\mu }_{0}i={\mu }_0\frac{i}{\pi R^2}\pi r^2$
$B.2\pi r=\frac{{\mu }_{0}i.\pi r^2}{\pi R^2}$
$\Rightarrow B\alpha r$