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

A wire \(X\) of length \(50\; cm\) carrying a current of \(2\,A\) is placed parallel to a long wire \(Y\) of length \(5\,m\). The wire \(Y\) carries a current of \(3\,A\). The distance between two wires is \(5\,cm\) and currents flow in the same direction. The force acting on the wire \(Y\) is.

A \(1.2 \times 10^{-5} \;N\) directed towards wire \(X\).
B \(1.2 \times 10^{-4}\;N\) directed away from wire \(X\).
C \(1.2 \times 10^{-4}\; N\) directed towards wire \(X\).
D \(2.4 \times 10^{-5} \;N\) directed towards wire \(X\).

Verified Solution

Answer & Solution

Correct Answer

(A) \(1.2 \times 10^{-5} \;N\) directed towards wire \(X\).

Step-by-step Solution

Detailed explanation

Force of interaction \(=I_{1} \ell_{1} B_{12}\) \(=\frac{\mu_{0} I _{1} I _{2}}{2 \pi r } \ell_{1}\) \(=\frac{4 \pi \times 10^{-7} \times 6 \times 5}{2 \pi \times 5 \times 10^{-2}}\) \(=1.2 \times 10^{-5} \text { towards } X\)

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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