What does a toroid consist of ? Find out the expression for the magnetic field inside a toriod for N turns of the coil having an average radius r and carrying current I. show that the magnetic field in the open space inside and outside the torroid is zero.

Explanation

1st Part, See section `1.51.`
2nd Part, Circumference of the toroid `=2pir`
Number of turns per unit length `n=(N)/(2pir)`
Magnetic field inside the toroid, `B= mu_(0)nl=(mu_(0)NI)/(2pir)`
The currents in every pair of diametrically opposite points of the toroid is equal and opposite. so , if we tak Ampere's loops in the open space insdie and outside the toroid, the current enclosed by the loop are respectively, `0-0-and NI-NI=0` [Fig. 1.143]

So, from Ampere's circuital law, `oint vecB* dvecl= mu_(0)I`,
We have `B=0` in both the cases.