दो बहुत लम्बे, सीधे तथा विधुत रोधी तारों को एक दूसरे से \(90^{\circ}\) कोण पर चित्रानुसार \(x y\)-समतल में रखा है। तारों में एकसमान धारा I, चित्र में दिखायी दिशा में, बह रही है। बिन्दु \(P\) पर परिणामी चुम्बकीय क्षेत्र होगा :

A \(\frac{{{\mu _0}I}}{{2\pi d}}\left( {\hat x + \hat y} \right)\)
B \(\frac{{ + {\mu _0}I}}{{\pi d}}\left( {\hat z} \right)\)
C शून्य
D \(-\frac{{{\mu _0}I}}{{2\pi d}}\left( {\hat x + \hat y} \right)\)

Verified Solution

Answer & Solution

Correct Answer

(C) शून्य

Step-by-step Solution

Detailed explanation

Magnetic field at point \(P\) \(\overrightarrow{\mathrm{B}}_{\mathrm{net}}=\frac{\mu_{0} \mathrm{i}}{2 \pi \mathrm{d}}(-\hat{\mathrm{k}})+\frac{\mu_{0} \mathrm{i}}{2 \pi \mathrm{d}}(\hat{\mathrm{k}})=0\)

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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