Current flows through uniform, square frames as shown. In which case is the magnetic field at the centre of the frame not zero?
Diffcult
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$\mathrm{i}_{1}=\frac{3}{4} \mathrm{i} ; \quad \mathrm{i}_{2}=\frac{\mathrm{i}}{4}$
Let magnetic field due to sides of square be $B_{5}$ $B_{s}=\frac{-\mu_{0} \frac{3}{4} i_{1}}{4 \pi \frac{L}{2}}\left(\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{2}}\right) \hat{k}+\frac{3 \mu_{0} \frac{i}{4}}{4 \pi \frac{L}{2}}\left(\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{2}}\right)$
$\mathrm{B}_{3}=0$
But magnetic field due to $2$ infinitely long wires is not zero so net magnetic Field is zero.
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