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:......$\mu T$ [Take $\mu _0 = 4\pi \times 10^{-7}\,NA^{-2}$]
JEE MAIN 2019, Medium
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$i=10\, \mathrm{A}$
$\ell=1\, \mathrm{m}$
$\mu_{0}=4 \pi \times 10^{-7} \,\frac{\mathrm{N}}{\mathrm{A}^{2}}$
$\mathrm{B}=\frac{\mu_{0} \mathrm{i}}{\frac{4 \pi \sqrt{3} \ell}{2}} \times 3$
$=\frac{\mu_{0} \mathrm{i} \sqrt{3}}{2 \pi \ell}=\frac{4 \pi \times 10^{-7} \times 10 \times \sqrt{3}}{2 \pi \times 1}=20 \sqrt{3} \times 10^{-7}$
$=3 \,\mu \mathrm{T}$
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