Two wires carrying

Options

A. Parallel current repel each other.
B. Antiparallel current attract each other.
C. Antiparallel current repel each other.
D. Equal magnitudes of antiparallel current attract each other.

Answer

To solve the problem regarding the forces between two wires carrying currents, we can break down the solution into clear steps.

### Step-by-Step Solution:

1. **Understanding the Setup**:
- We have two long parallel wires. Let’s denote them as Wire 1 and Wire 2.
- Wire 1 carries a current \( I_1 \) and Wire 2 carries a current \( I_2 \).

2. **Direction of Currents**:
- For the first case, assume both wires carry currents in the same direction (parallel currents).
- For the second case, assume the currents are in opposite directions (antiparallel currents).

3. **Magnetic Field Due to a Current-Carrying Wire**:
- The magnetic field \( B \) created by a long straight wire at a distance \( r \) from it is given by:
\[ B = \frac{\mu_0 I}{2 \pi r} \]
- Here, \( \mu_0 \) is the permeability of free space.

4. **Force on a Current-Carrying Wire**:
- The force \( F \) on a segment of wire of length \( L \) carrying current \( I \) in a magnetic field \( B \) is given by:
\[ F = I L \times B \]
- The direction of the force can be determined using the right-hand rule.

5. **Calculating the Force for Parallel Currents**:
- For Wire 1, the magnetic field at the location of Wire 2 (due to Wire 1) is:
\[ B_1 = \frac{\mu_0 I_1}{2 \pi r} \]
- The force on Wire 2 due to Wire 1 is:
\[ F_{12} = I_2 L B_1 = I_2 L \left(\frac{\mu_0 I_1}{2 \pi r}\right) \]
- The direction of this force is attractive (both wires pull towards each other).

6. **Calculating the Force for Antiparallel Currents**:
- For antiparallel currents, the magnetic field direction remains the same, but the force direction changes.
- The force on Wire 2 due to Wire 1 is still given by:
\[ F_{12} = I_2 L B_1 = I_2 L \left(\frac{\mu_0 I_1}{2 \pi r}\right) \]
- However, this time the force is repulsive (the wires push away from each other).

7. **Conclusion**:
- For parallel currents, the force is attractive.
- For antiparallel currents, the force is repulsive.

### Final Answer:
- Parallel currents attract each other, while antiparallel currents repel each other.