Question

A toroid has a core (non-ferromagnetic) of inner radius 25 cm and outer radius 26 cm, around which 3,500 turns of a wire are wound. If the current in the wire is 11 A, then what is the magnetic field (in Tesla) inside the core of the toroid?

Answer 1

Mean radius of the toroid,
$r=\frac{\text{inner radius}+\text{outer radius}}{2}$

$\Rightarrow r=\frac{25+26}{2}=25.5\times {10}^{-2}m$

The total length of the toroid,

$l=2\pi r=2\pi \times 25.5\times {10}^{-2}$
$\Rightarrow l=51\pi \times {10}^{-2}m$

Number of turns per unit length,
$n=\frac{\text{total no.of turns}}{\text{total length}}$

$\Rightarrow n=\frac{3500}{51\pi \times {10}^{-2}}$

Magnetic field inside the toroid,
$B={\mu }_{0}ni$

$\Rightarrow B=4\pi \times {10}^{-7}\times \frac{3500}{51\pi \times {10}^{-2}}\times 11$

$\Rightarrow B=0.03T$

Therefore, magnetic field is 0.03 T.