A loop ABCDA , carrying current $\mathrm{I}=12 \mathrm{~A}$, is placed in a plane, consists of two semi-circular segments of radius $R_1=6 \pi \mathrm{~m}$ and $\mathrm{R}_2=4 \pi \mathrm{~m}$. The magnitude of the resultant magnetic field at center O is $\mathrm{k} \times 10^{-7} \mathrm{~T}$. The value of k is ______ (Given $\mu_0=4 \pi \times 10^{-7} \mathrm{Tm} \mathrm{A}^{-1}$)

Question

Aicharya · Accepted Answer

Magnetic field due to $\mathrm{AB} \& \mathrm{CD}=0$
$\begin{aligned}
& \mathrm{B}_0=\left|\mathrm{B}_{\mathrm{R}_1}-\mathrm{B}_{\mathrm{R}_2}\right| \\ & =\frac{\mu_0 \mathrm{I}}{4 \mathrm{R}_2}-\frac{\mu_0 \mathrm{I}}{4 \mathrm{R}_1} \\ & =\frac{4 \pi \times 10^{-7} \times 12}{4}\left(\frac{1}{4 \pi}-\frac{1}{6 \pi}\right) \\ & =12 \pi \times 10^{-7}\left(\frac{1}{12 \pi}\right) \\ & =1 \times 10^{-7}
\end{aligned}$
$K=1$

A loop ABCDA , carrying current $\mathrm{I}=12 \mathrm{~A}$, is placed in a plane, consists of two…

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