Two parallel wires carrying current in the same direction attract each other while two beams of electrons travelling in the same direction repel each other. Why?

Options

A. (a) potential difference between them
B. (b) mutual inductance between them
C. (c) electric force between them
D. (d) magnetic force between them

Answer

To understand why two parallel wires carrying current in the same direction attract each other while two beams of electrons traveling in the same direction repel each other, we can break down the explanation into several steps.

### Step-by-Step Solution:

1. **Understanding Current in Wires**:
- When we have two parallel wires carrying current, the direction of the current in both wires is the same. Let's denote the current in both wires as flowing downwards.

2. **Magnetic Field Created by a Current-Carrying Wire**:
- A current-carrying wire generates a magnetic field around it. The direction of this magnetic field can be determined using the right-hand rule. If you point your thumb in the direction of the current, your fingers will curl in the direction of the magnetic field lines.

3. **Magnetic Field Interaction**:
- For the first wire (Wire 1), the magnetic field it creates at the location of the second wire (Wire 2) will be directed into the page (or screen). Conversely, Wire 2 also creates a magnetic field that affects Wire 1.

4. **Force on the Wires**:
- According to Fleming's Left-Hand Rule, the force experienced by a current-carrying conductor in a magnetic field can be determined. The direction of the force is such that both wires experience an attractive force towards each other when the currents are in the same direction.

5. **Electrons in Beams**:
- Now, consider two beams of electrons traveling in the same direction. Electrons have a negative charge, and the conventional current is defined as the flow of positive charge. Therefore, the current due to these beams of electrons is actually in the opposite direction to the flow of electrons.

6. **Current Direction in Electron Beams**:
- If both beams of electrons are moving to the right, the equivalent current for each beam is directed to the left. Thus, the two beams of electrons are effectively carrying currents in opposite directions.

7. **Magnetic Field from Electron Beams**:
- Just like with the wires, each beam of electrons generates a magnetic field around it. However, since the currents (due to the electron flow) are in opposite directions, the magnetic fields created by each beam will also interact differently.

8. **Force Between Electron Beams**:
- Using Fleming's Left-Hand Rule again, we find that the force between the two beams of electrons is repulsive because they are carrying currents in opposite directions. Therefore, the beams repel each other.

### Conclusion:
In summary, two parallel wires carrying current in the same direction attract each other due to the interaction of their magnetic fields, while two beams of electrons traveling in the same direction repel each other because they effectively carry currents in opposite directions.

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