Toroid has a core (non-ferromagnetic) of inner radius 25 cm and outer radius 26 cm, around which 3500 turns of a wire wound. If the current in the wire is 11A, what is the magnetic field (a) outside the toroid, (b) inside the core of the toroid, and (c) in the empty space surrounded by the torroid.

Explanation

(a) The magnetic field is zero outside the toroid
(b) The magnetic field inside the toroid for n number of turns per unit length and current I flowing through its coil is given by:
`B = mu_(0)nI`
If r is the mean radius of toroid and N is the total number of turns, then:
` n = N/(2 pi r)`
` rArr " " B = mu_(0) xx N/(2 pi r) I`
Here, `r = (26 + 25)/2 = 25.5 cm = 25.5 xx 10^(-2) m`
` N = 3,500`
` I = 11 A`
`rArr " " B = (4pi xx 10^(-7))/(2 pi) xx (3,500 xx 11)/((25.5)/100)`
` = (2 xx 10^(-7) xx 35 xx 11 xx 10^(5))/(255) `
` = (2 xx 10^(-7) xx 35 xx 11 xx 10^(5))/(255) `
` :. " " B = 3.02 xx 10^(-2) T`
Magnetic field in the empty space surrounded by the toroid is zero.