Force acting on two parallel current-carrying conductors is __________, if the current is in the same direction.

Force Acting on Two Parallel Current-Carrying Conductors

Definition: When two parallel current-carrying conductors are placed near each other, they exert a force on each other due to the interaction of their magnetic fields. The direction and nature of this force depend on the direction of the currents in the two conductors. If the currents flow in the same direction, the force is attractive, and if the currents flow in opposite directions, the force is repulsive.

Working Principle:

The phenomenon can be explained using Ampere's law and the Biot-Savart law:

• Each conductor generates a magnetic field around it due to the flow of current. The magnetic field produced by a current-carrying conductor at a distance r from it is given by:

B = (μ₀ × I) / (2π × r)

• Here, B is the magnetic field, μ₀ is the permeability of free space, I is the current, and r is the distance from the conductor.
• The second conductor, placed in the magnetic field of the first conductor, experiences a force due to the magnetic field. This force is given by:

F = I × L × B

• Here, F is the force, L is the length of the conductor, and B is the magnetic field.

Substituting the value of B into the formula for force:

F = (μ₀ × I₁ × I₂ × L) / (2π × r)

• Here, I₁ and I₂ are the currents in the two conductors, and r is the distance between them.

The direction of the force can be determined using the right-hand rule. If the currents in the two conductors are in the same direction, the force is attractive. If the currents are in opposite directions, the force is repulsive.

Correct Option Analysis:

The correct option is:

Option 4: Attractive

When the currents in the two parallel conductors flow in the same direction, the magnetic fields around the conductors interact in such a way that the conductors attract each other. This phenomenon is a direct consequence of the magnetic field interaction and is consistent with the principles of electromagnetism.

The force of attraction can be calculated using the formula:

F = (μ₀ × I₁ × I₂ × L) / (2π × r)

• Here, F is the attractive force per unit length of the conductors.
• μ₀ is the permeability of free space (4π × 10⁻⁷ H/m).
• I₁ and I₂ are the currents in the two conductors.
• L is the length of the conductors.
• r is the distance between the conductors.

This formula highlights that the force is proportional to the product of the currents and inversely proportional to the distance between the conductors.

Additional Information

To further understand the analysis, let’s evaluate the other options:

Option 1: Zero

This option is incorrect because the force is not zero. The magnetic fields produced by the currents interact with each other, resulting in a force between the conductors. The force can only be zero if the currents are zero or the conductors are infinitely far apart, which is not the case here.

Option 2: Infinite

This option is incorrect because the force cannot be infinite. The force depends on the currents, the distance between the conductors, and the permeability of free space, all of which are finite quantities under normal circumstances.

Option 3: Repulsive

This option is incorrect because the force is repulsive only when the currents in the two conductors flow in opposite directions. In this case, since the currents are in the same direction, the force is attractive.

Option 5: (No Option Provided)

This option is not valid because it does not contain any relevant information or alternative explanation for the phenomenon.

Conclusion:

The force acting on two parallel current-carrying conductors is attractive if the currents flow in the same direction. This attractive force arises from the interaction of the magnetic fields generated by the currents in the conductors. Understanding this concept is essential for applications in electromagnetism, such as in the design of electrical machines and power transmission systems.