The magnitude of the magnetic field (B) due to the loop

Question:

The magnitude of the magnetic field (B) due to the loop $\mathrm{ABCD}$ at the origin $(\mathrm{O})$ is :-

A current loop ABCD is held fixed on the plane of the paper as shown in the figure. The arcs BC (radius $=b$ ) and DA (radius $=a$ ) of the loop are joined by two straight wires AB and CD. A steady current $\mathrm{I}$ is flowing in the loop. Angle made by $\mathrm{AB}$ and $\mathrm{CD}$ at the origin $\mathrm{O}$ is $30^{\circ}$. Another straight thin wire with steady current $I_{1}$ flowing out of the plane of the paper is kept at the origin.

  1. $\frac{\mu_{0} \mathrm{I}}{4 \pi}\left[\frac{\mathrm{b}-\mathrm{a}}{\mathrm{ab}}\right]$

  2. $\frac{\mu_{0} I}{4 \pi}\left[2(b-a)+\frac{\pi}{3}(a+b)\right]$

  3. Zero

  4. $\frac{\mu_{0} \mathrm{l}(\mathrm{b}-\mathrm{a})}{24 \mathrm{ab}}$


Correct Option: , 4

Solution:

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