Force and deflection of moving charges

Key idea: A magnetic field pushes a moving charge perpendicular to its motion. It can bend a beam without changing particle speed, and crossed fields can select one velocity.

GCE A-Level H1 Physics 2027

H1 Physics 8867 · Lesson 3 of 3

Check your understanding

By the end of this lesson, you should be able to

Predict magnetic-force direction for positive and negative charges.
Use F = BQv sin θ and analyse electric and magnetic beam deflection.
Derive and apply the velocity-selector condition v = E/B.

Learn the idea

Big question: How can a magnetic force bend a moving particle without changing its speed?

Use charge sign after finding the positive direction

For a positive charge, treat its velocity as conventional current in Fleming's left-hand rule. Reverse the predicted force for a negative charge. The magnitude is F = BQv sinθ, using charge magnitude Q.

No magnetic force acts when velocity is parallel to B. For perpendicular motion, force is perpendicular to velocity and can continually turn the particle.

Check your understanding: A positive and negative particle have the same velocity in the same field. Compare their force directions.

They are opposite if the charge magnitudes are equal; the sign reverses the force.

Compare electric and magnetic deflection

A perpendicular magnetic force does no work because it has no component along displacement. It changes velocity direction but not speed or kinetic energy.

In crossed perpendicular fields arranged to oppose, an undeflected particle satisfies QE = BQv, so v = E/B. For a negative charge both forces reverse, so the selected speed is unchanged and does not depend on mass or charge magnitude.

Check your understanding: Does a magnetic field transfer energy to a charged particle?

No. Magnetic force is perpendicular to motion and does no work.

Scroll diagram horizontally to read all labels.

For a positive charge, the electric and magnetic forces oppose. Only v = E/B makes their magnitudes equal; slower and faster particles bend to opposite sides.

Key ideas

No magnetic force acts for motion parallel to B.
Reverse the force direction when the charge sign reverses.
Velocity selection depends on E and B, not on mass or charge magnitude.

Relationships to know

Fmagnetic = BQv sin θ
magnetic work = 0
velocity selector: v = E/B

Follow the reasoning

Worked example

Use crossed fields as a velocity selector

Question: A beam passes undeflected through E = 4.5 × 10⁴ N C⁻¹ and B = 0.18 T. Find its speed. A positive ion at 20% greater speed enters: state which force is larger and how it deflects if electric force points upward.

Step 1: Balance forces for the selected beam
Why: No deflection means the opposing electric and magnetic forces are equal.
Working: QE = BQv, so v = E/B = 4.5 × 10⁴/0.18 = 2.50 × 10⁵ m s⁻¹.
Step 2: Compare the faster ion
Why: Electric force is speed-independent but magnetic force is proportional to speed.
Working: At 1.20v, Fmagnetic = 1.20QE, so it exceeds electric force.
Step 3: Use the stated orientation
Why: If electric force is upward, the balancing magnetic force is downward.
Working: The stronger magnetic force makes the faster positive ion deflect downward.

Answer: Selected speed is 2.50 × 10⁵ m s⁻¹. A 20% faster positive ion deflects in the magnetic-force direction, downward here.

Check: Charge cancels from the selector condition, but it still matters when assigning the two force directions.

Now try it with support

Practise with support

A positive ion moves east through a magnetic field directed north. State its force direction, then state the direction for an electron moving the same way.

Hints

Use conventional current east for the positive ion.
Reverse the result for negative charge.

View the guided answer

The positive ion is forced upward. The electron is forced downward because its charge is negative.

Your turn

Practise independently

A proton enters crossed fields E = 3.0 × 10⁴ V m⁻¹ and B = 0.20 T. Find the undeflected speed and state how an electron at that speed behaves.

Check your answer

The undeflected speed is v = E/B = (3.0 × 10⁴)/0.20 = 1.5 × 10⁵ m s⁻¹. An electron with the same velocity is also undeflected: its electric and magnetic forces both reverse, so they remain equal and opposite.

Common mistakes and exam guidance

Watch out for

Saying a magnetic field increases speed because it exerts a force.
Predicting that an electron at v = E/B deflects because only one of the two forces reverses.

In an exam

Find the positive-charge direction first, then reverse for a negative charge.
For beam questions, state separately whether speed, direction and kinetic energy change.

Put the ideas together

Exam-style practice [7 marks]

An electron moves at 6.0 × 10⁶ m s⁻¹ perpendicular to a 0.25 T field. Find the force magnitude using e = 1.60 × 10⁻¹⁹ C. Explain what happens to speed, velocity and kinetic energy, and compare this with an electric field parallel to its motion.

Plan before you answer

Use charge magnitude for force size and sign for direction.
Separate speed from velocity.
Decide whether each force can do work.

View the marking points and model answer

Marking points

Uses F = BQv.
Obtains 2.4 × 10⁻¹³ N.
States magnetic force is perpendicular to velocity.
States speed remains constant.
States velocity direction changes.
States kinetic energy remains constant/no magnetic work.
Explains a parallel electric force can change speed and kinetic energy, with direction depending on electron sign.

Model answer

F = 0.25(1.60 × 10⁻¹⁹)(6.0 × 10⁶) = 2.4 × 10⁻¹³ N. The magnetic force is perpendicular to velocity, so it turns the electron: velocity changes but speed and kinetic energy remain constant because no work is done. An electric field parallel to the motion gives an electron force opposite the field; depending on the orientation it speeds or slows the electron and therefore changes kinetic energy.

Finish from memory

Three-question recap

Write magnetic force on a moving charge.
Check
F = BQv sinθ.
Why does magnetic force do no work?
Check
It is perpendicular to the particle's displacement.
What speed passes undeflected through a velocity selector?
Check
v = E/B.

Try this next

Compare trajectories in electric-only, magnetic-only and crossed-field regions using labelled sketches.

Check the whole topic Return to Electromagnetism Review Magnetic fields and force on a conductor

Continue with the next resource in this course.

Course and syllabus information

Course: GCE A-Level H1 Physics
Edition: GCE A-Level H1 Physics 2027