Question 24 of 276
A loop ABCDA , carrying current , is placed in a plane, consists of two semi-circular segments of radius and . The magnitude of the resultant magnetic field at center O is . The value of k is ______ (Given )
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Answer: 1
Magnetic field due to
$\begin{aligned}
& \mathrm{B}_0=\left|\mathrm{B}_{\mathrm{R}_1}-\mathrm{B}_{\mathrm{R}_2}\right| \\
& =\frac{\mu_0 \mathrm{I}}{4 \mathrm{R}_2}-\frac{\mu_0 \mathrm{I}}{4 \mathrm{R}_1} \\
& =\frac{4 \pi \times 10^{-7} \times 12}{4}\left(\frac{1}{4 \pi}-\frac{1}{6 \pi}\right) \\
& =12 \pi \times 10^{-7}\left(\frac{1}{12 \pi}\right) \\
& =1 \times 10^{-7}
\end{aligned}$
$\begin{aligned}
& \mathrm{B}_0=\left|\mathrm{B}_{\mathrm{R}_1}-\mathrm{B}_{\mathrm{R}_2}\right| \\
& =\frac{\mu_0 \mathrm{I}}{4 \mathrm{R}_2}-\frac{\mu_0 \mathrm{I}}{4 \mathrm{R}_1} \\
& =\frac{4 \pi \times 10^{-7} \times 12}{4}\left(\frac{1}{4 \pi}-\frac{1}{6 \pi}\right) \\
& =12 \pi \times 10^{-7}\left(\frac{1}{12 \pi}\right) \\
& =1 \times 10^{-7}
\end{aligned}$
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