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.
Inside the toroid :
Let us calculate the magnetic field `B_(S) ` at point S by constructing an Amperian loop 2 of radius `r_(2)` around the point S as shown in Figure. The length of the loop is `L_(2) = 2 pi r_(2)`
Ampere's circuital law for the loop 2 is
`underset("loop2")oint vecB_(s) . vec(dl) =mu_(0)I_("enclosed")`
Let I be the current passing through the toroid and N be the number of turns of the toroid, then
` I_("enclosed") = NI `
and `underset("loop2")oint vecB_(s) . vec(dl) =underset("loop2")ointB dl cos theta = B 2 pi r_(2)`
`underset("loop2")ointvecB_(s) . vec(dl) = mu_(0) NI `
` B_(s) = mu_(0) (NI)/(2 pi r_(2))`
The number of turns per unit length is `n = N/(2 pi r_(2))` , then the magnetic field at point S is
` B_(s) = mu_(0) n I`