Step 1: Understanding the Concept:
When an electric current flows through a long, straight conductor, it generates a circular magnetic field around itself according to the Biot-Savart Law.
If another current-carrying conductor is placed in this magnetic field, it will experience a magnetic force.
This is an application of the principle that a magnetic field exerts a force on a moving charge or a current-carrying wire.
The direction of the magnetic field produced by a wire can be determined using the Right-Hand Thumb Rule.
The direction of the force experienced by the other wire can then be determined using Fleming's Left-Hand Rule or the Right-Hand Palm Rule.
Step 2: Detailed Explanation:
Let's consider two parallel wires, Wire 1 and Wire 2, placed close to each other. Both carry current in the upward direction.
1. Magnetic Field of Wire 1: If we point the thumb of our right hand upwards (current direction), our fingers curl around the wire. At the position of Wire 2, the magnetic field produced by Wire 1 (\(B_{1}\)) points "into the plane of the page."
2. Force on Wire 2: Now we apply Fleming's Left-Hand Rule to Wire 2:
- Point your index finger into the page (direction of \(B_{1}\)).
- Point your middle finger upwards (direction of the current in Wire 2).
- Your thumb will naturally point to the left, which is toward Wire 1.
3. Symmetry: By Newton's Third Law, if Wire 1 exerts a force on Wire 2 toward itself, Wire 2 must also exert an equal and opposite force on Wire 1. Thus, Wire 1 will be pulled toward Wire 2.
Because both wires are being pulled toward each other, the resulting interaction is "attraction."
If the currents were in opposite directions, the forces would be directed away from each other, leading to "repulsion."
This physical principle is used to define the unit of current, the Ampere.
One Ampere is defined as the current that, if maintained in two straight parallel conductors of infinite length and negligible circular cross-section, and placed one meter apart in vacuum, would produce between these conductors a force equal to \(2 \times 10^{-7}\) Newtons per meter of length.
Step 3: Final Answer:
Two parallel wires carrying currents in the same direction experience a mutual force of attraction.
Therefore, the correct option is (B).