Question

A toroid has a core (non-ferromagnetic) of inner radius 25 cm and outer radius 26 cm, around which 2,000 turns of a wire are wound. If the current in the wire is 10 A, the magnetic field inside the core of the toroid will be ______

Options

• 31.4 x 10^-2 T

• 31.4 x 10^-3 T

• 15.7 x 10^-2 T

• 15.7 x 10^-3 T

Answer 1

A toroid has a core (non-ferromagnetic) of inner radius 25 cm and outer radius 26 cm, around which 2,000 turns of a wire are wound. If the current in the wire is 10 A, the magnetic field inside the core of the toroid will be 15.7 x 10^-3 T.

Explanation:

I = 10 A;

Total number of turns = 2000

Mean radius of the toroid,

r = `(25 + 26)/2` = 25.5 cm = `25.5 xx 10^-2` m

Total length (circumference) of the toroid

= `2pir = 2pi xx 25.5 xx 10^-2 = 51 pi xx 10^-2` m

Therefore, number of turns per unit length,

n = `2000/(51pi xx 10^-2)`

The field inside the core of the toroid,

B = `mu_0"nI" = 4pi xx 10^-7 xx 2000/(51pi xx 10^-2) xx 10`

= `15.7 xx 10^-3` T