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The question in the image refers to a situation where an electric field is directed "into the page." This is typically associated with the magnetic field when we analyze a charged particle's motion in an electric and magnetic field setup.

### Why is the field into the page?
From the context, it seems that you're dealing with the motion of a charged particle (likely an electron, \(e^{-}\), based on the negative charge) under the influence of an electric field and a magnetic field.

1. **Electric Field (\(E\))**: In the diagram, there are positively charged particles (\(+\)) on one side and negatively charged particles (\(-\)) on the other. The electric field (\(E\)) would naturally point from the positive charges to the negative charges, creating a force on the negatively charged electron in the opposite direction (because the force on a charge in an electric field is \( \vec{F}_e = q\vec{E} \)). So, the electric field is drawn upwards in this case, opposite to the electron's movement.

2. **Magnetic Field (\(B\))**: According to the right-hand rule (for conventional positive charge) or the left-hand rule (for electron motion), if the electron is moving perpendicular to both the electric and magnetic fields, a magnetic force will act on the electron. In this scenario, the direction of the magnetic field is drawn as "into the page."

3. **Explanation Using Right-Hand Rule**:
   - The magnetic field into the page can be explained using the **Right-Hand Rule** for a positive charge, or alternatively the **Left-Hand Rule** for an electron:
     - Point your fingers in the direction of the velocity of the particle.
     - Point your palm towards the direction of the magnetic field.
     - The direction your thumb points will give you the direction of the force (Lorentz force \( F_m = q \vec{v} \times \vec{B} \)).
   
   Since the electron has a negative charge, the magnetic force will be in the opposite direction. This creates a situation where the magnetic force and electric force act in opposite directions, balancing each other out.

4. **Magnetic Force and Field Direction**: 
   The diagram suggests that:
   - \( \vec{F}_e \), the electric force, points downward (because the electron feels a force opposite to the electric field).
   - \( \vec{F}_m \), the magnetic force, is directed upwards, which is equal and opposite to \( \vec{F}_e \), hence they balance.
   - For this to happen, the magnetic field must be directed into the page, as indicated in the diagram.

This is why the magnetic field direction is "into the page" — it ensures that the magnetic force opposes the electric force, thus balancing the forces on the electron.

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Would you like more details or have any specific questions? Here are a few follow-up questions to consider:

1. How does the right-hand rule apply to different particle charges?
2. What is the relationship between the velocity, magnetic field, and the Lorentz force?
3. What happens if the magnetic field is reversed in direction (out of the page)?
4. How does this situation change for a positively charged particle instead of an electron?
5. Can you describe the motion of a particle when both electric and magnetic forces are present?

**Tip**: When solving electromagnetic problems, use the right-hand rule to determine the directions of forces, and remember that the forces on negative and positive charges are opposite!

Why is the magnetic field direction into the page?

Learn why the magnetic field direction is into the page in problems involving electric and magnetic fields acting on charged particles. This includes the application of the right-hand rule and Lorentz force, suitable for Grades 11-12 physics students.

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