બે લાંબા \(8\,A\) અને \(15\,A\) વીજ પ્રવાહ ધારિત સમાંતર તારને એકબીજાથી \(7\,cm\) ના અંતરે રખેલ છે. બંને તારથી સમાન અંતરે બિંદુ \(P\) એવી રીતે આવેલું છે કે જેથી બિંદુ \(P\) ને તાર સાથે જોડતી રેખાઓ પરસ્પર લંબ થાય. તો \(P\) બિંદુુએ ચુંબકીય ક્ષેત્રનું મૂલ્ય \(............\times 10^{-6} T\) છે. \(\left(\sqrt{2}=1.4\right)\) આપેલું છે.

A \(65\)
B \(68\)
C \(66\)
D \(67\)

Verified Solution

Answer & Solution

Correct Answer

(B) \(68\)

Step-by-step Solution

Detailed explanation

Magnetic fields due to both wires will be perpendicular to each other. \(B _1=\frac{\mu_0 i _1}{2 \pi d } \quad B _2=\frac{\mu_0 i _2}{2 \pi d }\) \(B _{\text {net }}=\sqrt{ B _1^2+ B _2^2} \Rightarrow \frac{\mu_0}{2 \pi d } \sqrt{ i _1^2+ i _2^2}\)…

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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