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Question: Answered & Verified by Expert
An arangement with a pair of quarter circular coils of radii $r$ and $R$ with a common centre $C$ and carrying a current $I$ is shown.


The permeability of free space is $\mu_{0}$. The magnetic field at $C$ is
PhysicsMagnetic Properties of MatterKVPYKVPY 2013 (SB/SX)
Options:
  • A $\mu_{0} \mid(1 / r-1 / R) / 8$ into the page
  • B $\mu_{0} \mid(1 / r+1 / R) / 8$ out of the page
  • C $\mu_{0} \mid(1 / r-1 / R) / 8$ out of the page
  • D $\mu_{0} \mid(1 / r+1 / R) / 8$ into the page
Solution:
2140 Upvotes Verified Answer
The correct answer is: $\mu_{0} \mid(1 / r-1 / R) / 8$ out of the page
$B$ due to Arc $=\frac{\mu_{0} i \theta}{4 \pi r}$ $\frac{\mu_{0} i}{8}\left[\frac{1}{r}-\frac{1}{R}\right]$ out of the page

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