Question 282: Magnetism and Matter

Question

The magnetic field at the centre of a wire loop formed by two semicircular wires of radii $$R_1=2 \pi \mathrm{m}$$ and $$R_2=4 \pi \mathrm{m}$$, carrying current $$\mathrm{I}=4 \mathrm{~A}$$ as per figure given below is $$\alpha 	imes 10^{-7} \mathrm{~T}$$. The value of $$\alpha$$ is ________. (Centre $$\mathrm{O}$$ is common for all segments)

Accepted Answer

$$\begin{aligned}
& \frac{\mu_0 \mathrm{i}}{2 \mathrm{R}_2}\left(\frac{\pi}{2 \pi}ight) \otimes+\frac{\mu_0 \mathrm{i}}{2 \mathrm{R}_1}\left(\frac{\pi}{2 \pi}ight) \otimes \
& \left(\frac{\mu_0 \mathrm{i}}{4 \mathrm{R}_2}+\frac{\mu_0 \mathrm{i}}{4 \mathrm{R}_1}ight) \otimes \
& \frac{4 \pi 	imes 10^{-7} 	imes 4}{4 	imes 4 \pi}+\frac{4 \pi 	imes 10^{-7} 	imes 4}{4 	imes 2 \pi} \
& =3 	imes 10^{-7}=\alpha 	imes 10^{-7} \
& \alpha=3
\end{aligned}$$

Magnetism and Matter

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