Question 30 of 276

A current of 5A exists in a square loop of side $\frac{1}{\sqrt{2}} \mathrm{~m}$. Then the magnitude of the magnetic field $B$ at the centre of the square loop will be $p \times 10^{-6} \mathrm{~T}$. where, value of p is _____ .
$\left[\right.$ Take $\left.\mu_0=4 \pi \times 10^{-7} \mathrm{TmA}^{-1}\right]$.

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Answer: 8

Let B be the magnetic field due to single side
$\begin{aligned}
& \text { then } B=\frac{\mu_0 \mathrm{i}}{4 \pi \mathrm{~d}}\left(\sin \theta_1+\sin \theta_2\right) \\
& =\frac{10^{-7} \times 5 \times 2}{\frac{1}{2 \sqrt{2}}} \times \frac{1}{\sqrt{2}}=2 \times 10^{-6} \\
& \therefore B_{\text {net }} \text { at centre } O=4 B \\
& =8 \times 10^{-6}
\end{aligned}$