A toroid has a core (non-ferromagnetic) of inner radius 25 cm and… - Vidyadip

Question

A toroid has a core $($non$-$ferromagnetic$)$ of inner radius $25 \ cm$ and outer radius $26 \ cm,$ around which $3500$ turns of a wire are wound. If the current in the wire is $11 A,$ what is the magnetic field,

Outside the toroid,
Inside the core of the toroid and,
In the empty space surrounded by the toroid.

✓

Answer

Inner radius of the toroid, $r_1 = 25 \ cm = 0.25 m$
Outer radius of the toroid, $r_2 = 26 \ cm = 0.26 m$
Number of turns on the coil, $N = 3500$
Current in the coil, $I = 11 A$

Magnetic field outside a toroid is zero. It is non$-$zero only inside the core of a toroid.
Magnetic field inside the core of a toroid is given by the relation.

$\text{B}=\frac{\mu_{0}\text{NI}}{l}$
Where,
$\mu_{0}=$ Permeability of free space $=4\pi\times10^{-7}\text{T mA}^{-1}$
$l =$ length of toroid
$2\pi\Big[\frac{\text{r}_{1}+\text{r}_{2}}{2}\Big]$
$\pi(0.25+0.26)$
$\therefore\text{B}=\frac{4\pi\times10^{-7}\times3500\times11}{0.51\pi}$
$≈ 3.0 \times 10^{-2} T$

Magnetic field in the empty space surrounded by the toroid is zero.

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