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Question: Answered & Verified by Expert
If a current I is flowing in a loop of radius $\mathrm{r}$ as shown in adjoining figure, then the magnetic field induction at the centre $\mathrm{O}$ will be
PhysicsMagnetic Effects of CurrentVITEEEVITEEE 2013
Options:
  • A Zero
  • B $\frac{\mu_{0} I \theta}{4 \pi r}$
  • C $\frac{\mu_{0} I \sin \theta}{4 \pi r}$
  • D $\frac{2 \mu_{0} I \sin \theta}{4 \pi r^{2}}$
Solution:
2824 Upvotes Verified Answer
The correct answer is: $\frac{\mu_{0} I \theta}{4 \pi r}$
Magnetic field $\mathrm{B}=\frac{\mu_{0}}{4 \pi} \frac{2 \pi \mathrm{I}}{\mathrm{r}}$
Here, $2 \pi=\theta$
$\therefore \mathrm{B}=\frac{\mu_{0}}{4 \pi} \frac{\theta I}{I}$

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