KCET · Physics · Magnetic Effects of Current

Two parallel wires in free space are \(10 \mathrm{~cm}\) apart and each carries a current of \(10 \mathrm{~A}\) in the same direction. The force exerted by one wire on the other [per unit length] is

A \(2 \times 10^{-4} \mathrm{Nm}^{-1}\) [attractive]
B \(2 \times 10^{-7} \mathrm{Nm}^{-1}\) [attractive]
C \(2 \times 10^{-4} \mathrm{Nm}^{-1}\) [repulsive]
D \(2 \times 10^{-7} \mathrm{Nm}^{-1}\) [repulsive]

Verified Solution

Answer & Solution

Correct Answer

(A) \(2 \times 10^{-4} \mathrm{Nm}^{-1}\) [attractive]

Step-by-step Solution

Detailed explanation

Given,
\(\begin{aligned}
&r=10 \mathrm{~cm}=10 \times 10^{-2} \mathrm{~m} \\
&I_{1}=I_{2}=10 \mathrm{~A}
\end{aligned}\)
Force exerted by one wire on the other per unit length is given as
\(\frac{F}{l}=\frac{\mu_{0} I_{1} I_{2}}{2 \pi r}\)
Substituting the given values, in the above relation, we get
\(\frac{F}{l}=\frac{4 \pi \times 10^{-7} \times 10 \times 10}{2 \pi \times 10 \times 10^{-2}}=2 \times 10^{-4} \mathrm{Nm}^{-1}\)
Since, the current is flowing in the same direction, so the force will be attractive in nature.

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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