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A toroid has a core of inner radius 20cm...

A toroid has a core of inner radius `20cm` and outer radius `22cm` around which `4200` turns of a wire are wound. If the current in the wire is `10A`, what is the magnetic field
(a) inside the core of toroid (b) outside the toroid
(c) in the empty space surrounded by toroid?

A

0.04 T

B

`0.04 xx 10^(-2)` T

C

400 gauss

D

Both (a) & (c)

Text Solution

Verified by Experts

The correct Answer is:
D
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 = 2pi r = 2pi xx 0.21` m
= 0.42 `pi` m
`therefore` No. of turns per unit length
`n = (4200)/(0.42 pi) = (10000)/(pi) m^(-1)`
`B = mu_(o) n I = 4pi xx 10^(-7) xx (10000)/(pi) xx 10`
B = 0.04 T (`because LT = 10^(4)` gauss)
= 0.04
B = 400 gauss
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