Question

A long, straight wire of diameter 2.0mm carries a uniformly distributed current of 10A. At what distance from the axis of the wire will the magnitude of B vector be maximum.justify your answer

Answer 1

For $0<r<R=2(mm)$

$\int Bdl=\mu_0I$

$B\cdot2\pi r=\mu_0\cdot \frac{I}{\pi R^2}\cdot\pi r^2\to B=\frac{\mu_0 I}{2\pi R^2}r$

For $r>R$

$B\cdot2\pi r=\mu_0 I\to B=\frac{\mu_0 I}{2\pi r}$

So, $B=B_{max}=\frac{\mu_0I}{2\pi R}$ if $r=R=2(mm)$ . Answer