To determine the correct answer, let’s analyze each particle's motion and the force exerted by the magnetic field. We'll use the right-hand rule for magnetic force:

• If the particle is positive, point your fingers in the direction of the velocity, curl them toward the magnetic field (B), and your thumb points in the direction of the force (F).
• If the particle is negative, the force direction will be the opposite of the right-hand rule.

Step-by-Step Analysis of Locations 1 to 4

1. Location 1:

   • The particle is negative and moving to the right ($v$) in the magnetic field ($B$) pointing into the page.
   • By the right-hand rule, the force on a positive charge would point up. Since the charge is negative, the force direction is down.

2. Location 2:

   • The particle is positive and moving to the left ($v$), with the magnetic field still pointing into the page.
   • Using the right-hand rule: velocity to the left, magnetic field into the page → force points up.

3. Location 3:

   • The particle is negative and moving rightward in the same magnetic field.
   • By the right-hand rule for a positive charge, the force would point up, but since the charge is negative, the force points down.

4. Location 4:

   • The particle is positive and moving upward ($v$), with the magnetic field still into the page.
   • Using the right-hand rule: velocity upward, magnetic field into the page → force points right.

Answer

The force directions at locations 1 to 4 are:

• 1: down
• 2: up
• 3: down
• 4: right

Thus, the correct answer is:

D. left; zero; down; right

Let me know if you need any clarification or further details!

Related Questions:

1. How does the right-hand rule work for magnetic forces on charged particles?
2. What happens to the force direction if the charge is reversed (positive vs negative)?
3. What does "magnetic field into the page" mean in diagrams?
4. How does velocity direction affect the force in a magnetic field?
5. What happens to the particle's path when the force is perpendicular to velocity?

Tip:

Always start by determining if the particle is positive or negative before applying the right-hand rule to avoid direction errors!