A wire in the form of a square of side ‘$a$’ carries a current $i$. Then the magnetic induction at the centre of the square wire is (Magnetic permeability of free space =${\mu _o}$)
Diffcult
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(c) ${B_0} = 4 \times \frac{{{\mu _0}}}{{4\pi }} \times \frac{i}{{\left( {a/2} \right)}}(\sin 45^\circ + \sin 45^\circ )$
$ = 4 \times \frac{{{\mu _0}}}{{4\pi }} \times \frac{{2i}}{a} \times \frac{2}{{\sqrt 2 }}$
$ = \frac{{{\mu _0}i2\sqrt 2 }}{{\pi a}}$
$ = 4 \times \frac{{{\mu _0}}}{{4\pi }} \times \frac{{2i}}{a} \times \frac{2}{{\sqrt 2 }}$
$ = \frac{{{\mu _0}i2\sqrt 2 }}{{\pi a}}$
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