\(I\) પ્રવાહ ધરાવતી એક વર્તુળાકાર લૂપની દ્વિદ્યુવી ચાકમાત્રા \(m\) છે.અને લૂપના કેન્દ્ર આગળ ચુંબકીયક્ષેત્ર \(B_1\) જેટલું છે.જયારે પ્રવાહ અચળ રાખીને દ્વિદ્યુવી ચાકમાત્રા બમણી કરવામાં આવે છે,ત્યારે લૂપના કેન્દ્ર આગળ ચુંબકીયક્ષેત્ર \(B_2\) થાય છે. \(\frac{{{B_1}}}{{{B_2}}}\) ગુણોત્તર ______.

A \(\sqrt 3 \)
B \(\sqrt 2 \)
C \(\frac{1}{{\sqrt 2 }}\)
D \(2\)

Verified Solution

Answer & Solution

Correct Answer

(B) \(\sqrt 2 \)

Step-by-step Solution

Detailed explanation

Magnetic field at the centre of \(\operatorname{loop}, B_{1}=\frac{\mu_{0} I}{2 R}\) Dipole moment of circular loop is \(m=I A\) \(\mathrm{m}_{1}=\mathrm{I} \cdot \mathrm{A}=\mathrm{I} \pi \mathrm{R}^{2} \quad\{\mathrm{R}=\text { Radius of the loop }\}\) If moment is doubled…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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