Question

Show that in an ideal toroid the magnetic field outside the toroid at any point in the open space is zero.

Answer 1

Let BB be the magnitude of the magnetic field along the Amperean loop 22 of radius rr.
Length of loop $2,L2=2\pi r$

If N is the total number of turns in the toroid and I the current in the toroid, then total current enclosed by the loop $2=NI$

Applying Ampere's circuital aw,

$B\times 2\pi r={\mu }^0\times NI$$

or $B={\mu }^{0}NI2\pi r$

If r be the average radius of the toroid and n the number of turns per unit length,then

$N=2\pi rn$

$B={\mu }^{0}ni$

$\therefore$ $B={\mu }^{0}nI$