The current of 5 A flows in a square loop of sides 1 m is placed in air. The magnetic field at the centre of the loop is X 2 × 10 - 7 T . The value of X is _________.

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TestHub · Accepted Answer

Magnetic field at the centre of the square loop is given by,
$B = 4 [\frac{μ_{0} I}{4 π d} (\sin 45 ° + \sin 45 °)]$ , where $d$ is perpendicular distance of the centre to one of its sides.
$\Rightarrow B = 4 \times \frac{μ_{0} \times 5}{4 π \times \frac{1}{2}} (\frac{1}{\sqrt{2}} + \frac{1}{\sqrt{2}})$
$= 4 \times 10^{- 7} \times 5 \times 2 \times \sqrt{2}$
$= 40 \sqrt{2} \times 10^{- 7} T$

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