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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?

Text Solution

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Here, inner radius, `r_1=20cm`.
Outer radius, `r_2=22cm`, `I=10A`
`:.` Mean radius of toroid,
`r=(r_1+r_2)/(2)=(20+22)/(2)=21cm=0*21m`
Total length of toroid=circumference of toroid
`=2pir=2pixx0*21`
`=0*42pim`
Total number of turns, `N=4200`
`:.` Number of turns per unit length will be,
`n=(4200)/(0*42pi)=(10000)/(pi)m^-1`
(a) Magnetic field induction inside the core of
toroid, `B=mu_0nI=4pixx10^-7x(10000)/(pi)xx10=0*04T`
(b) Magnetic field induction outside the toroid is zero, since the field is only confined inside the core of the toroid on which winding has been made.
(c) Magnetic field induction in the empty space surrounded by toroid is also zero.
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