Question:

Consider the circular loop having current $i$ and with central point $O$. The magnetic field at the central point $O$ is

Updated On: Jun 23, 2023
  • $\frac{2\mu_0 i}{3\pi R} $ acting downward
  • $ \frac{5\mu_0i}{12R}$ acting downward
  • $ \frac{6\,\mu_0 i}{11 R} $ acting downward
  • $\frac{3\mu_0 i}{7R}$ acting upward
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The Correct Option is B

Solution and Explanation

The angle subtended by circular part of the conduction is $3 \pi / 2$ or $270^{\circ}$. The net magnetic field at point $O$ is $B_{\text {net }}=B_{1}+B_{2}$ where, $B_{1}=$ magnetic field due to arc $II$ and $B_{2}=$ magnetic field due to arc $I$ $\Rightarrow B_{\text {net }} =\frac{\mu_{0} i}{4 \pi \times 3 R} \times \frac{\pi}{2}+\frac{\mu_{0} i}{4 \pi R} \times 3 \frac{\pi}{2} $ $=\frac{5 \mu_{0} i}{12 R} $ ( downward ) .
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Magnets are used in many devices like electric bells, telephones, radio, loudspeakers, motors, fans, screwdrivers, lifting heavy iron loads, super-fast trains, especially in foreign countries, refrigerators, etc.

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Some of the properties of the magnetic field lines are:

  • The lines and continuous and outside the magnet, the field lines originate from the North pole and terminate at the South pole
  • They form closed loops traversing inside the magnet. 
  • But here the lines seem to originate from the South pole and terminate at the North pole to form closed loops.
  • More number of close lines indicate a stronger magnetic field
  • The lines do not intersect each other
  • The tangent drawn at the field line gives the direction of the field at that point.