Use magnetic force on a moving charge
Calculate magnetic force on a moving charge and determine its direction from the velocity and field vectors.
A Level; Cambridge International Physics 9702, 2025–2027 syllabus, Topic 20. These original explanations and calculations are study aids; full timed assessment and human subject-teacher review remain outstanding.
Before you begin
- Use current, charge, force, velocity, vectors, area and SI units; distinguish conventional current from electron flow.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
A charge moves parallel to a magnetic field. What is the magnetic force magnitude?
What you will learn
- Use F = BQv sin θ
- Determine the force direction on a positive or negative moving charge
- Identify when magnetic force is zero or maximum
Only motion across the field produces magnetic force
A moving charge Q in a magnetic field B experiences force F = BQv sin θ in magnitude, where θ is the angle between velocity and field. For motion parallel to B the force is zero; for motion perpendicular to B it is greatest.
For a positive charge, the force direction is perpendicular to both velocity and magnetic field and can be found with the right-hand rule or by using conventional current in Fleming's left-hand rule. A negative charge feels force in the opposite direction.
The force is perpendicular to motion
Magnetic force is at right angles to the instantaneous velocity. It changes the direction of motion, but an ideal magnetic force does no work on the charge and does not change its speed.
The scalar equation gives a magnitude. Determine direction separately and check the charge sign. If the velocity is at an angle, only its component perpendicular to B contributes to the force.
Pause and explain
A negative particle moves in the same direction as a positive particle through the same field. How do their magnetic force directions compare?
Worked example
A +2.0 μC charge moves at 5.0 × 10³ m s⁻¹ perpendicular to a 0.20 T field. Find the force magnitude.
Show the worked solution
- Use F = B|Q|v sin θ.
- For perpendicular motion, sin θ = 1.
- Convert microcoulombs to coulombs.
Answer F = 0.20 × 2.0 × 10⁻⁶ × 5.0 × 10³ = 2.0 × 10⁻³ N.
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Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
A 3.0 nC charge moves at 2.0 × 10⁶ m s⁻¹ perpendicular to a 0.15 T field. Calculate the magnetic force magnitude.
Give me a hint
Convert nC to C and use sin 90° = 1.
Compare my reasoning
- Q = 3.0 × 10⁻⁹ C.
- F = 0.15 × 3.0 × 10⁻⁹ × 2.0 × 10⁶.
- F = 9.0 × 10⁻⁴ N.
F = 9.0 × 10⁻⁴ N.
Look for these in your work
- Charge converted
- Perpendicular relation used
- Magnitude calculated
An electron moves east while the magnetic field points north. State the direction of force on the electron.
Give me a hint
Find the direction for a positive charge first, then reverse it for an electron.
Compare my reasoning
- For a positive charge, use the right-hand rule with velocity east and field north.
- The positive-charge force is vertically out of the east–north plane (upward).
- An electron is negative, so its force is opposite: downward into the plane.
The force is downward into the plane, opposite the positive-charge direction.
Look for these in your work
- Positive reference direction established
- Charge sign applied
- Final direction stated
A particle's speed remains constant as it moves through a magnetic field, but its path curves. Explain how this is possible.
Give me a hint
Use the perpendicular direction of magnetic force relative to velocity.
Compare my reasoning
- The magnetic force is perpendicular to the instantaneous velocity.
- A perpendicular force changes velocity direction but does no work.
- The path curves while the speed remains constant.
The field changes the direction of velocity without changing its magnitude, so the path curves at constant speed.
Look for these in your work
- Force–velocity geometry stated
- Work consequence explained
- Curved motion reconciled
Common mistakes
- Applying magnetic force to a stationary charge
- Using the angle between force and field rather than v and B
- Giving a negative force magnitude for a negative particle
- Claiming a perpendicular magnetic force changes speed
What can you explain now?
A charge moves parallel to a magnetic field. What is the magnetic force magnitude?
Compare with the explanation
Zero
The perpendicular velocity component is zero.
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Make it stick
Why can a magnetic field bend a charged particle's path without changing its speed?
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