$A$ long thin hollow metallic cylinder of radius '$R$' carries a current '$i$'. The magnetic induction '$B$' at a distance '$r$' from the axis varies as shown in:

  • A
    Option A
  • B
    Option B
  • C
    Option C
  • D
    Option D

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The magnetic field at point $O$ for the given circuits is provided. Which of the following is correct?
$(i)$ $(ii)$ $(iii)$
$(A). \frac{\mu_0 i}{2r} \odot$ $(A). \frac{\mu_0}{2\pi} \frac{i}{r}(\pi - 2)$ $(A). \frac{\mu_0}{2r} \frac{2i}{r}(\pi + 1) \otimes$
$(B). \frac{\mu_0 i}{2r} \otimes$ $(B). \frac{\mu_0 i}{4\pi} \frac{i}{r}(\pi + 2) \otimes$ $(B). \frac{\mu_0 i}{4r} \frac{2i}{r}(\pi - 1) \otimes$
$(C). \frac{3\mu_0 i}{8r} \otimes$ $(C). \frac{\mu_0 i}{4r} \otimes$ $(C). \text{Zero}$
$(D). \frac{3\mu_0 i}{8r} \odot$ $(D). \frac{\mu_0 i}{4r} \odot$ $(D). \text{Infinite}$

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