Question

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 1

Here, I = 11 A,
total numbers of turns = 3,500
Mean radius of toroid,

(a) The field is non-zero only inside the core surrounded by the windings of the toroid. Therefore, the field outside the toroid is zero.
(b) The field inside the core of the toroid,

(c) For the above-mentioned reason, the field in the empty space surrounded by the toroid is also zero.

Answer 2

(a)The magnetic field outside is zero. It is nonzero only inside the core of a toroid.

By definition, Ampere's Law states that integration of magnetic field over an amperian loop is equivalent to constant μ multiplied by current enclosed. Now, the current that flows at the outer circumference and the inner circumference of the toroid is in opposite directions to each other. Therefore, currently enclosed by the Amperian loop is zero. Thus, a magnetic field outside the toroid is zero.

(b)Magnetic field inside the core of a toroid is given by the relation 

\(B= μ0 ​ nI/I ​ \)

l=length of toroid

where,\( l=2 π(r 1 ​ +r 2 ​ )/2 ​ =.51π\)

\(B= 4π×10-7 ×3500×11 ​ \) SORRY IT IS 10^-7 NOT 10-7

So B=3x10^-2 T

(c)Magnetic field in the empty space surrounded by the toroid is zero as there will no current in the empty space.