A toroidal coil has a core of inner radius 24 cm and outer radius 26 cm around which 2500 turns of a wire are wound. If the current in the wire is 10 A, what is the magnetic field (a) inside the core of the toroid (b) outside the toroid (c) in the empty space surrounded by toroid ?

Explanation

Here, `I = 10 A `
Total number of turns, `N= 2500`
Mean radius of toroid,
`r = ("Iriner radius + Outer radius ")/2 `
`= (24 + 26)/2 = 25 cm = 25 xx 10^(-2) m`
Total length of toroid = Circiumference of toroid
`= 2 pi r = 2 pi xx 25 xx 10^(-2) m`
`= 50 pi xx 10^(-2) m`
`therefore` Number of turns per unit length,
`n = (2500)/(50 pi xx 10^(-2)) = (50000)/(pi) m^(-1)`
(a) Magnetic field inside the core of the toroid,
`B = mu_0 nI`
`= 4pi xx 10^(-7) xx (5000)/pi xx 10 = 2 xx 10^(-2) T`
(b) As the field is only confined inside the core surrounded by the windings of the toroid, so the field outside the toroid is zero.
(c) For the same reason as given in (b), magnetic field in the empty space surrounded by the toroid is also zero.