Magnetic Effects Of Current Question 6
Question 6 - 2024 (27 Jan Shift 2)
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 $I=4 \mathrm{~A}$ as per figure given below is $\alpha \times 10^{-7} \mathrm{~T}$. The value of $\alpha$ is (Centre
$\mathrm{O}$ is common for all segments)
Show Answer
Answer: (3)
Solution:
$\frac{\mu_{0} \mathrm{i}}{2 \mathrm{R}{2}}\left(\frac{\pi}{2 \pi}\right) \otimes+\frac{\mu{0} \mathrm{i}}{2 \mathrm{R}_{1}}\left(\frac{\pi}{2 \pi}\right) \otimes$
$\left(\frac{\mu_{0} \mathrm{i}}{4 \mathrm{R}{2}}+\frac{\mu{0} \mathrm{i}}{4 \mathrm{R}_{1}}\right) \otimes$
$\frac{4 \pi \times 10^{-7} \times 4}{4 \times 4 \pi}+\frac{4 \pi \times 10^{-7} \times 4}{4 \times 2 \pi}$
$=3 \times 10^{-7}=\alpha \times 10^{-7}$
$\alpha=3$
