બે સમકેન્દ્રીય રિંગો એક જ સમતલમાં રહે તેમ ગોઠવેલ છે. દરેક રિંગમાં આંટાઓની સંખ્યા 25 છે. તેમની ત્રિજ્યાઓ 50 cm અને 200 cm છે. તથા તેમનામાંથી અનુક્રમે 0.1 A અને 0.2 A વિધુતપ્રવાહ પરસ્પર વિરુદ્ધ દિશામાં વહે છે, તો કેન્દ્ર પાસે ઉદ્ભવતાં ચુંબકીયક્ષેત્રનું મૂલ્ય __________ T થશે.

A \(4 \mu_0\)
B \(2 \mu_0\)
C \(\frac{10}{4} \mu_0\)
D \(\frac{5}{4} \mu_0\)

Verified Solution

Answer & Solution

Correct Answer

(D) \(\frac{5}{4} \mu_0\)

Step-by-step Solution

Detailed explanation

D
\(\begin{aligned} N & =25 \\ a_1 & =50 cm \\ a_2 & =200 cm \\ 11 & =0.1 A \\ 12 & =1.2 A\end{aligned}\)
\(B _{6 \sigma}=\frac{\mu_0 NI }{2 a}\) પરથી
\(\begin{array}{l}B=B_1-B_2 \\ B=\frac{\mu_0 N}{2}\left[\frac{I_1}{a_1}-\frac{I_2}{a_2}\right] \\ B=\frac{\mu_0 \times 25}{2}\left[\frac{0.1}{0.5}-\frac{0.2}{2}\right] \\ B=\frac{\mu_0 \times 25}{2}\left[\frac{1}{5}-\frac{1}{10}\right] \\ B=\frac{\mu_0 \times 25}{2}\left[\frac{1}{10}\right] \\ B=\frac{5}{4} \mu_0\end{array}\)

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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