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Question: Answered & Verified by Expert
A current carrying circular loop of radius $R$ is placed in the $x-y$ plane with centre at the origin. Half of the loop with $x>$ 0 is now bent so that it now lies in the $y-z$ plane.
PhysicsMagnetic Effects of Current
Options:
  • A
    The magnitude of magnetic moment now diminishes
  • B
    The magnetic moment does not change
  • C
    The magnitude of $B$ at $(0,0, z), z>R$ increases
  • D
    The magnitude of $\mathrm{B}$ at $(0,0, \mathrm{z}), \mathrm{z}>>\mathrm{R}$ is unchanged
Solution:
1621 Upvotes Verified Answer
The correct answer is:
The magnitude of magnetic moment now diminishes
As the direction of magnetic moment of circular loop of radius $R$ placed in the $x-y$ plane is along $z$-direction and given by $M=I\left(\pi r^2\right)$, when half of the loop with $x>0$ is now bent so that it now lies in the $y-z$ plane, the magnitudes of magnetic field moment of each semicircular loop of radius R lie in the $\mathrm{x}$-y plane and the $y$-z plane is $\mathrm{M}^{\prime}=\mathrm{I}\left(\pi \mathrm{r}^2\right) / 4$ and the direction of magnetic field moments are along zdirectlon and $\mathrm{x}$-direction respectively.
Then resultant is:
$$
\mathrm{M}_{\text {net }}=\sqrt{\mathrm{M}^{\prime 2}+\mathrm{M}^{\prime 2}}=\sqrt{2} \mathrm{M}^{\prime}=\sqrt{2} \mathrm{I}\left(\pi \mathrm{r}^2\right) / 4
$$
So, $\mathrm{M}_{\text {net }} < \mathrm{M}$ or $\mathrm{M}$ diminishes.
Hence, the magnitude of magnetic moment is now diminishes.

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