JEE Mains · Physics · STD 12 - 4. Moving charges and magnetism

There are two infinitely long straight current carrying conductors and they are held at right angles to each other so that their common ends meet at the origin as shown in the figure given below. The ratio of current in both conductor is \(1: 1\). The magnetic field at point \(P\) is ...... .

A \(\frac{\mu_{0} I}{4 \pi x y}\left[\sqrt{x^{2}+y^{2}}+(x+y)\right]\)
B \(\frac{\mu_{0} I}{4 \pi x y}\left[\sqrt{x^{2}+y^{2}}-(x+y)\right]\)
C \(\frac{\mu_{0} I x y}{4 \pi}\left[\sqrt{x^{2}+y^{2}}-(x+y)\right]\)
D \(\frac{\mu_{0} I x y}{4 \pi}\left[\sqrt{x^{2}+y^{2}}+(x+y)\right]\)

Verified Solution

Answer & Solution

Correct Answer

(A) \(\frac{\mu_{0} I}{4 \pi x y}\left[\sqrt{x^{2}+y^{2}}+(x+y)\right]\)

Step-by-step Solution

Detailed explanation

\({B}_{\text {due to wire }(1)}=\frac{\mu_{{o}} {I}}{4 \pi {y}}\left[\sin 90+\sin \theta_{1}\right]\) \(=\frac{\mu_{0}}{4 \pi} \frac{{I}}{{y}}\left(1+\frac{{x}}{\sqrt{{x}^{2}+{y}^{2}}}\right) \ldots \ldots(1)\)…

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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