આપેલ સ્થાને પૃથ્વીના ચુંબકીય ક્ષેત્રનો સમક્ષિતિજ ઘટક \(3.5 \times 10^{-5} \mathrm{~T}\) છે. દક્ષિણ-પૂર્વ થી ઉત્તર-પશ્ચિમ દિશામાં \(\sqrt{2} \mathrm{~A}\) પ્રવાહ ધરાવતા એક ખૂબ લાંબા સીધા સુવાહકને મૂકવામાં આવે છે. સુવાહક દ્વારા એકમ લંબાઈ દિઠ અનુભવાતું બળ _______ \(\times 10^{-6} \mathrm{~N} / \mathrm{m}\) છે.

A \(35\)
B \(15\)
C \(74\)
D \(64\)

Verified Solution

Answer & Solution

Correct Answer

(A) \(35\)

Step-by-step Solution

Detailed explanation

\( B_H=3.5 \times 10^{-5} T \) \( F=i \ell B \sin \theta, \quad \mathrm{i}=\sqrt{2} A \) \( \frac{F}{\ell}=i B \sin \theta=\sqrt{2} \times 3.5 \times 10^{-5} \times \frac{1}{\sqrt{2}} \) \( =35 \times 10^{-6} \mathrm{~N} / \mathrm{m}\)

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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