The magnitude of the magnetic field at the centre of an equilateral triangular loop of side 1 m which is carrying a current of 10 A is ____ (in $\mathrm{\mu T})$ [take ${\mathrm{\mu }}_0=4\mathrm{\pi }\times {10}^{-7} {\mathrm{NA}}^{-2}]$

Given data:

Current i=10 A

Length=1 m

Concepts used : moving charges and magnetism

Explanation:

The magnetic field at the center of an equilateral triangle

$3\left[\frac{{\mu }_{0i}}{4\pi r}\right[\sin 60+\sin 60\left]\right]$

Here $r=\frac{a}{2\sqrt{3}}$

$r=\frac{1}{2\sqrt{3}}$

B=$3 \{$$\frac{4\pi \times {10}^{-7}\times 10\times 2\sqrt{3}}{4\mathrm{\pi }}$}$[\frac{\sqrt{3}}{2}+\frac{\sqrt{3}}{2}]$

$B=18\times {10}^{-6}$

$B=18\mu T$

Therefore the correct answer is 18.