Question

A permanent magnet has the shape of a sufficiently thin disc magnetized along its axis. The radius of the disc is $R=1.0cm$. Evaluate the magnitude of a molecular current $I^{\prime }$ flowing along the rim of the disc if the magnetic induction at the point on the axis of the disc, lying at a distance $x=10cm$ from its centre, is equal to $B=30\mu T$.

Answer 1

For $x\gg R$,
$B_x\approx \frac{{\mu }_0{I}^{\prime }{R}^2}{2x^3}$
or, $I^{\prime }\approx \frac{2B_x{x}^3}{{\mu }_0{R}^2}=\frac{2\times 3\times {10}^{-5}T\times {\left({10}^{-1}m\right)}^3}{1.26\times {10}^{-6}\times {\left({10}^{-2}m\right)}^4}\approx 0.5kA$