Two parallel very long straight wires carrying current of 5 A each are kept at a separation of 1 m . If the currents are in the same direction, the force per unit length between them is _________. \(\frac{ N }{m}\). \(\left(\mu_0=4 \pi \times 10^{-7} SI \right)\)

A \(5 \times 10^{-5}\), attractive
B \(5 \times 10^{-6}\), attractive
C \(5 \times 10^{-5}\), repulsive
D \(5 \times 10^{-6}\), repulsive

Verified Solution

Answer & Solution

Correct Answer

(B) \(5 \times 10^{-6}\), attractive

Step-by-step Solution

Detailed explanation

B
Force per unit length,
\(\frac{F}{l}=\frac{\mu_0 I_1 I_2}{2 \pi y}\)
\(\begin{array}{l}\therefore \quad \frac{ F }{l}=\frac{4 \pi \times 10^{-7} \times 5 \times 5}{2 \pi \times 1} \\ \therefore \quad \frac{F}{l}=50 \times 10^{-7} \\ \therefore \quad \frac{F}{l}=5 \times 10^{-6} \frac{N}{ m } \cdot \text { attractive }\end{array}\)

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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