MCQ
Magnetic field at the centre $O$ due to the given structure is
  • A
    $\frac{\mu_0 l}{4 R}\left[\frac{3}{2}+\frac{1}{\pi}\right] \odot$
  • B
    $\frac{\mu_0 I}{2 R}\left[3+\frac{1}{\pi}\right] \otimes$
  • $\frac{\mu_0 I}{4 R}\left[\frac{3}{2}+\frac{1}{\pi}\right] \otimes$
  • D
    $\frac{\mu_0 l}{4 R}\left[3+\frac{2}{\pi}\right] \odot$

Answer

Correct option: C.
$\frac{\mu_0 I}{4 R}\left[\frac{3}{2}+\frac{1}{\pi}\right] \otimes$
c
(c)

$B=B_{\text {due to circular arc }}+B_{\text {due to straight wires }}$

$=\frac{\mu_0 i}{2 R}\left(\frac{3 \pi}{2 \cdot(2 \pi)}\right)+\frac{\mu_0 i}{4 \pi R}$

$\Rightarrow B=\frac{\mu_0 i}{4 R}\left(\frac{3}{2}+\frac{1}{\pi}\right) \otimes$

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