Question

Two straight parallel conductors of 5 m length each and separated by a distance of 1 cm in free space carry currents of 2A and 3A, respectively, in the same direction. The force per unit length on either of the conductor is

• A. an attractive force of \(1.2 \times 10^{-4} \text{ Nm}^{-1}\)
• B. a repulsive force of \(1.2 \times 10^{-4} \text{ Nm}^{-1}\)
• C. a repulsive force of \(6 \times 10^{-4} \text{ Nm}^{-1}\)
• D. an attractive force of \(6 \times 10^{-4} \text{ Nm}^{-1}\)
• E. a repulsive force of \(4\pi \times 10^{-7} \text{ Nm}^{-1}\)

Hint:

Like poles repel, like charges repel, but LIKE currents attract. This is a common point of confusion for students. Always remember same direction = attraction.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
Parallel currents flowing in the same direction attract each other, while currents in opposite directions repel each other. The force between them is due to the interaction of the magnetic field of one conductor with the current in the other.

Step 2: Key Formula or Approach:
Force per unit length: \(f = \frac{\mu_0 I_1 I_2}{2\pi d}\)
where \(\mu_0 = 4\pi \times 10^{-7} \text{ T m/A}\).

Step 3: Detailed Explanation:
Given:
\(I_1 = 2 \text{ A}\), \(I_2 = 3 \text{ A}\)
\(d = 1 \text{ cm} = 0.01 \text{ m}\)
Direction: Same (Attractive force).
Calculating magnitude:
\[ f = \frac{(4\pi \times 10^{-7}) \times 2 \times 3}{2\pi \times 0.01} \]
\[ f = \frac{2 \times 10^{-7} \times 6}{10^{-2}} \]
\[ f = 12 \times 10^{-5} = 1.2 \times 10^{-4} \text{ Nm}^{-1} \]

Step 4: Final Answer:
The force is an attractive force of \(1.2 \times 10^{-4} \text{ Nm}^{-1}\).