Question

A toroid has a core of inner radius 20 cm and outer radius 22 cm around which 4200 turns of a wire are wound. If the current in the wire is 10 A. What is the magnetic field inside the core of toroid?

Options

• 0.04 T

• 0.04 × 10^-3 T

• 400 gauss

• Both 0.04 T and 400 gauss

Answer 1

Both 0.04 T and 400 gauss

Explanation:

Inner radius = 20 cm, outer radius = 22 cm mean radius of the toroid = `("r"_1 + "r"_2)/2 = (20 + 22)/2`

r = 21 cm

r = 0.21 m

Total length of toroid = circumference

L = 2πr = 2π × 0.21 m

= 0.42 π m

∴ No. of turns per unit length

n = `4200/(0.42  pi) = 10000/pi " m"^-1`

B = `mu_0 "nI" = 4pi xx 10^-7 xx 10000/pi xx 10`

B = 0.04 T

B = 400 gauss   (∵ 1 T = 10⁴ gauss)