A toroid has a non-ferromagnetic core of inner radius 20.5 cm and outer radius 21.5 cm, around which 4200 turns of a wire are wound. If the current in the wire is 10 A, the magnetic field inside the core of the toroid is `(mu_(0)=4pi times 10^(-7)Hm^(-1))`

Options

A. 20 mT
B. 40 mT
C. 20 `pi` mT
D. 40 `pi` mT

Answer

B

Explanation

Given, inner radius of non-ferromagnetic core, `r_(i)=20.5` cm
outer radius of non-ferromagnetic core, `r_(0)=21.5 cm`
mean radius of toroid, `r=(r_(i)+r_(0))/2=42/2=21cm`
number of turns of wire, N = 4200
and current in wire, I = 10 A
`" "mu_(0)=4pi times 10^(-7)Hm^(-1)`
`therefore` Circumference of core = length of the wire
`" "2pir=l`
Then, number of turns per unit length,
`" "N=n/l=n/(2pir)`
Now, magnetic field inside the core of the toroid is magnetic field, `B=mu_(0)NI`
`" "=4pi times 10^(-7) times n/(2pir) times 10`
`" "=2 times 10^(-7) times n/r timse 10`
`" "(because` Outer radius of core `r=21.5 cm)`
`B=2 times 10^(-7) times 4200/21 times 10`
`" "=40 times 10^(-3)=40 times 10^(-3)T`
`B=40mT`