What is Toroid? Calculate the magnetic field at a point
Open space exterior to the toroid

Explanation

A slolenoid is bent in a way that both their ends are joined together to form a closed ring shape, is called as toroid . The magnetic field has constant magnitude inside the toroid whereas in the interior region ( say , at point P ) and exterior rigion ( say , at point Q ) , the magnetic field is zero.
Open space interior to the toroid :
Let us calculate the magnetic field `B_(p) ` at point P. We construct an Amperian loop 1 of radius `r_(1)` around the point P as shown in Figure. For simplicity, we take circular loop so that the length of the loop is its circumference.

`L_(1) = 2 pi r_(1) `
Amperes circuital law for the loop 1 is
`underset("loop1")oint vecB_(p) . vec(dl) = mu_(0)I_("enclosed") `
Since , the `"loop"_(1)` encloses no current , `I_("enclosed") = 0 `
`underset("loop1")oint vecB_(p) . vec(dl) = 0`
This is possible only if the magnetic field at point P vanishes i.e.
`vecB_(p) = 0 `