Question

Two infinitely long straight parallel conductors carrying currents \(I_1\) and \(I_2\) are held at a distance d apart in vacuum. The force F on a length L of one of the conductors due to the other is _______.
Fill in the blank with the correct answer from the options given below

• A. proportional to L but independent of \( I_1\times I_2\)
• B. proportional to \(I_1 × I_2\) but independent of length L
• C. proportional to \(I_1 × I_2 × L\)
• D. proportional to\( \frac{L}{ I_1 × I_2}\)

Answer 1

The Correct Option is C

The force between two parallel conductors carrying currents is determined using equations derived from Ampère's Law and the Biot-Savart Law. For two parallel currents, I₁ and I₂, separated by a distance d in a vacuum, the force per unit length f is:

\( f = \frac{\mu_0}{2\pi} \cdot \frac{I_1I_2}{d} \)

Here, μ₀ represents the permeability of free space. The total force F on a conductor of length L is calculated as:

\( F = f \cdot L = \left(\frac{\mu_0}{2\pi} \cdot \frac{I_1I_2}{d}\right) \cdot L \)

This equation shows that the force F is directly proportional to the product I₁ × I₂ × L.

Consequently, the force on a length L of one conductor is proportional to \(I_1 \times I_2 \times L\).