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

$r_1=0.25m,r_2=0.26m,n=3500,I=11A$

(a)magnetic field outside is zero. It is non zero 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 outer circumference and inner circumference of toroid are in opposite direction to each other. Therefore, current enclosed by Amperian loop is zero. Thus, magnetic field outside the toroid is zero.

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

$B=\frac{{\mu }_{o}nI}{l}$

l=length of toroid

where, $l=2\frac{\pi (r_1+r_2)}{2}=.51\pi$ .

$B=\frac{4\pi \times {10}^{-7}\times 3500\times 11}{0.51\pi }$

so, $B=3\times {10}^{-2}T$

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