To analyze the statements provided in the question, we will evaluate each statement one by one based on the principles of electromagnetism.
### Step-by-Step Solution:
**Statement 1:** If a positive charge is thrown parallel to a current-carrying wire, it will be attracted by the wire.
1. **Understanding the Situation:**
- We have a current-carrying wire with current flowing in a specific direction.
- A positive charge is moving parallel to this wire.
2. **Magnetic Field Around the Wire:**
- A current-carrying wire generates a magnetic field around it. The direction of the magnetic field can be determined using the right-hand rule. If the current is flowing upwards, the magnetic field will circle around the wire.
3. **Force on the Moving Charge:**
- The force experienced by a moving charge in a magnetic field is given by the Lorentz force equation:
\[
\mathbf{F} = q(\mathbf{v} \times \mathbf{B})
\]
- Here, \( q \) is the charge, \( \mathbf{v} \) is the velocity of the charge, and \( \mathbf{B} \) is the magnetic field.
- Since the charge is positive and moving parallel to the current, it will experience a force due to the magnetic field.
4. **Conclusion for Statement 1:**
- The positive charge will indeed be attracted towards the wire due to the magnetic force acting on it.
- Therefore, **Statement 1 is true.**
---
**Statement 2:** If a negative charge is thrown antiparallel to a current-carrying wire, it will be repelled by the wire.
1. **Understanding the Situation:**
- We have a current-carrying wire with current flowing in a specific direction.
- A negative charge is moving in the opposite direction (antiparallel) to the current.
2. **Magnetic Field Around the Wire:**
- As established earlier, the magnetic field around the wire is still the same.
3. **Force on the Moving Charge:**
- Using the Lorentz force equation again, we analyze the force on the negative charge.
- Since the charge is negative, the direction of the force will be opposite to that calculated for a positive charge moving in the same direction.
4. **Conclusion for Statement 2:**
- The negative charge moving antiparallel to the current will also experience a force towards the wire, not away from it.
- Therefore, **Statement 2 is false.**
---
**Statement 3:** A current-carrying wire can apply a force on a charge placed near it.
1. **Understanding the Situation:**
- We consider a stationary charged particle placed near a current-carrying wire.
2. **Magnetic Field Around the Wire:**
- The wire generates a magnetic field, but the stationary charge does not have any velocity.
3. **Force on the Stationary Charge:**
- The magnetic force on a charge is dependent on its velocity. If the charge is stationary, then:
\[
F_B = q \cdot v \cdot B = 0
\]
- Since \( v = 0 \), the magnetic force is zero.
4. **Conclusion for Statement 3:**
- A current-carrying wire does not exert a magnetic force on a stationary charge.
- Therefore, **Statement 3 is false.**
---
### Final Conclusion:
- **Statement 1 is true.**
- **Statement 2 is false.**
- **Statement 3 is false.**
Thus, the correct option is **C** (only Statement 1 is true).
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