A current of 10 A flows through a horizontal straight wire \(A\) with both ends rigidly fixed. Wire B is placed directly above and parallel to A. The weight per unit length of wire \(B\) is \(40 \times 10^{-3} Nm ^{-1}\) and it carries a current of 20 A . Find the distance of the wire \(B\) from the wire \(A\) so that the wire \(B\) remains at rest. Also state the direction of current flowing through it.

A \(\frac{1}{3} \times 10^{-3} m\), both are in same direction
B \(\frac{1}{2} \times 10^{-3} m\), both are in opposite direction
C \(2 \times 10^{-3} m\), both are in same direction
D \(1 \times 10^{-3} m\), both are in opposite direction

Verified Solution

Answer & Solution

Correct Answer

(D) \(1 \times 10^{-3} m\), both are in opposite direction

Step-by-step Solution

Detailed explanation

D
\(\frac{ F }{l}=\frac{\mu_0 I _1 I _2}{2 \pi y}\)
\(\therefore 40 \times 10^{-3}=\frac{4 \pi \times 10^{-7} \times 10 \times 20}{2 \pi \times y}\)
\(\therefore \quad y=\frac{2 \times 10^{-7} \times 10 \times 20}{40 \times 10^{-3}}\)
\(y=10^{-3} m\)
Current will flow in opposite directions.

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.

Same subject

Explore more questions on app

From GUJCET

Explore more questions on app