A toroid has a core (non-ferromagnetic) of inner radius 25 cm and outer radius 26 cm, around which 3500 turns of a wire are wound. If the current in the wire is 11 A, 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 toroid.

Explanation

(a)
Applying Ampere-Maxwell circuital law to Amperean loop-1 (outside the toroid)
`ointvecB*vec(dl)=mu_(0)(sumI)`
= `mu_(0)(-NI+NI)`
= 0
`thereforeB=0` (Outside the toroid)
(b) Magnetic field inside the toroid (which has the volume and shape like circular inflated tube also called toroidal region) is,
`B=mu_(0)NI`
= `mu_(0)(N/(2pir))I" "("Where "r=(r_(1)+r_(2))/2)`
`thereforeB=((4pixx10^(-7))(3500)(11))/((2pi)((0.25+0.26)/2))`
`thereforeB=3.02xx10^(-2)T`
(In a direction, tangential to a circle of radius r, inside the toroid)
( c) Applying Ampere-Maxwell circuital law to Amperian loop-2, surrounded by toroid,
`ointvecB*vec(dl)=mu_(0)(sumI)`
= `mu_(0)(0)`
= 0
`thereforeB=0`
(In the region surrounded by toroid)