Find magnetic field at centre $P$ if length of side of square loop is $20\, cm$
AIIMS 2019, Medium
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The length of the square loop is: $a=20 cm$
The distance from corner to $P$ is,
$r=a \sqrt{a}$
The magnetic field at centre $P$ is,
$B=\frac{\mu_{0} i}{\pi a} r$
$=\frac{\mu_{0} i}{\pi a} a \sqrt{a}$
$=\frac{4 \times 10^{-7} \times 3}{\pi \times 0.2}(0.2 \sqrt{0.2})$
$=120 \sqrt{2} \times 10^{-7}$
$=12 \sqrt{2} \times 10^{-6} T$
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