Question 554 of 949
What is the direction of the magnetic force experienced by a straight current-carrying conductor placed in a uniform magnetic field, given that the current flows from left to right and the magnetic field is directed into the page?
- Upward
- Downward
- Towards the left
- Towards the right
Correct Answer:
A
Explanation
### Correct Option: A. Upward
### Detailed Explanation:
To determine the direction of the magnetic force experienced by a straight current-carrying conductor in a magnetic field, we can use the **right-hand rule**. This rule is a helpful mnemonic for visualizing the relationship between the direction of the current, the magnetic field, and the resulting magnetic force.
#### Step-by-Step Explanation:
1. **Identify the Directions**:
- The current is flowing from **left to right**.
- The magnetic field is directed **into the page** (often represented by dots or crosses in diagrams).
2. **Applying the Right-Hand Rule**:
- Extend your right hand.
- Point your thumb in the direction of the current (which is from left to right).
- Point your fingers in the direction of the magnetic field (which is into the page).
- Your palm will then face in the direction of the magnetic force acting on the conductor.
3. **Resulting Direction**:
- When you apply the right-hand rule as described, your palm will face **upward**. This indicates that the magnetic force acting on the conductor is directed **upward**.
### Why the Other Options are Incorrect:
- **Option B: Downward**:
- If the magnetic force were downward, it would contradict the application of the right-hand rule. The thumb (current) and fingers (magnetic field) do not align to produce a downward force.
- **Option C: Towards the left**:
- A leftward force would also contradict the right-hand rule. The current and magnetic field directions do not produce a leftward force.
- **Option D: Towards the right**:
- Similarly, a rightward force is not possible with the given directions of current and magnetic field. The right-hand rule clearly shows that the force is directed upward.
### Formulas and Concepts:
The magnetic force \( F \) on a straight conductor can be calculated using the formula:
\[
F = I \cdot L \cdot B \cdot \sin(\theta)
\]
Where:
- \( F \) is the magnetic force,
- \( I \) is the current,
- \( L \) is the length of the conductor in the magnetic field,
- \( B \) is the magnetic field strength,
- \( \theta \) is the angle between the current direction and the magnetic field direction.
In this case, since the current and magnetic field are perpendicular to each other (90 degrees), \( \sin(90^\circ) = 1 \), simplifying the formula to:
\[
F = I \cdot L \cdot B
\]
### Common Pitfalls:
- **Misapplying the Right-Hand Rule**: It's crucial to remember that the thumb represents the current, the fingers represent the magnetic field, and the palm indicates the force. Confusing these can lead to incorrect conclusions.
- **Forgetting the Direction of the Magnetic Field**: Always ensure you know the direction of the magnetic field before applying the right-hand rule.
- **Assuming Forces Without Analysis**: Always analyze the situation using the right-hand rule or the formula rather than guessing the direction of the force.
### Revision Summary:
- Use the right-hand rule to determine the direction of the magnetic force on a current-carrying conductor.
- Thumb = current direction, fingers = magnetic field direction, palm = force direction.
- In this case, with current left to right and magnetic field into the page, the force is upward.
- Always check the angles and directions carefully to avoid mistakes.