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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. |
Answer» Solution :(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) |
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