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Guidance on Magnetic Force Direction for Charges in a Magnetic Field

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Q1. Determine the direction of the force on the charge due to the magnetic field.

Background

Topic: Magnetic Force on Moving Charges

This question tests your understanding of how a charged particle experiences a force when moving through a magnetic field, specifically the direction of that force as described by the Lorentz force law.

Key Terms and Formulas

  • Magnetic Force:

  • Where:

    • = charge of the particle

    • = velocity vector of the particle

    • = magnetic field vector

    • = cross product (determines direction using the right-hand rule)

Right-hand rule for magnetic force direction

Step-by-Step Guidance

  1. Identify the direction of the velocity vector and the magnetic field vector for the charge in the diagram or description.

  2. Recall that the direction of the force is given by the cross product , which is perpendicular to both and .

  3. Use the right-hand rule: Point your fingers in the direction of , curl them toward , and your thumb points in the direction of the force for a positive charge.

  4. If the charge is negative, the force direction is opposite to your thumb.

  5. Set up the possible answer choices based on the orientation of and (e.g., out of the page, into the page, left, right, etc.).

Try solving on your own before revealing the answer!

Final Answer:

The direction of the force is determined by the right-hand rule for a positive charge, and opposite for a negative charge. For example, if is to the right and is into the page, the force on a positive charge points upward; for a negative charge, it points downward.

This follows from and the right-hand rule.

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