Theme D — Fields

D.3.3 Magnetic Force on a Charge — IB Physics HL Revision Notes & Topical Questions

5 min read 9 parts Lesson 30 of 39 1 quiz

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Lesson summary

D.3.3 Magnetic Force on a Charge — IB PHYSICS SL notes: Calculate the magnetic force on a moving charged particle and find its direction.Condition — a magnetic field acts only on a moving charge, and a stationary charge feels no magnetic forceA moving charge produces its own magn…

Perpendicular motion
What the symbols mean
Parallel motion
Changing direction
Mixing up equations
Mutually perpendicular

Part 1 of 7The force on a single charge

Condition

Condition a magnetic field acts only on a moving charge, and a stationary charge feels no magnetic force

A moving charge produces its own magnetic field, which interacts with the applied field

Equation

F = qvB sin θ
F is the magnetic force in N.
q is the charge in C; for an electron q = −1.60 × 10⁻¹⁹ C.
v is the speed in m s⁻¹.
B is the magnetic flux density in T.
θ is the angle between the velocity and the field.

Perpendicular motion

Perpendicular motion at θ = 90° the force is maximum, F = qvB
What the symbols mean: F = force on the moving charge (N) · B = magnetic flux density (T) · q = charge (C) · v = speed (m s⁻¹)

Parallel motion

Parallel motion when v is parallel to B there is no force
The particle keeps going in a straight line, so it can travel freely along a field line.

Changing direction

Changing direction if the direction of motion changes, the size of the force changes too

Mixing up equations

F = BIL is for a current-carrying conductor and F = qvB is for an isolated moving charge, which may be inside a conductor

Part 2 of 7Direction of the force

Mutually perpendicular

F, B and v are at right angles, so the force is perpendicular to both the motion and the field

Fleming's left-hand rule

Fleming's left-hand rule thumb along the force, first finger along the field and second finger along the conventional current

Positive charge

Positive charge the current points in the direction of its velocity

Negative charge

Negative charge the current points opposite to its velocity, so the force is reversed relative to a positive charge moving the same way
For an electron beam moving left in a field into the page, the current points right and the force is upward.

Not the right-hand rule

Fleming's right-hand rule is for generators, while the left-hand rule is for motors

Part 3 of 7No work is done

Reason

Reason the force is always at right angles to the velocity, so the displacement along the force is zero

Result

Result the kinetic energy and speed do not change
Only the direction of motion changes.

Summary

Summary a magnetic field bends a charge but never speeds it up

Part 4 of 7Link to the force on a wire

Link to the force on a wire

A charge q crossing a length L at speed v takes time t = L/v.

The current is I = q/t, so IL = qv.

Substituting into F = BIL gives F = Bqv.

Meaning

F = qvB sin θ is the fundamental form, and F = BIL sin θ is its sum over many charges

Solid conductor

Solid conductor the force acts on the carriers and they pass it to the lattice through collisions

Hall effect

Hall effect a sideways build-up of charge across a current-carrying strip gives a Hall voltage that depends on B

Part 5 of 7Paths in a field

Entering at an angle

Entering at an angle the velocity splits into a component along B, which is unaffected, and a component perpendicular to B, which is rotated
The result is a helical path (D.3.4).

Perpendicular entry

Perpendicular entry the path is a circle

Circular motion

Circular motion the magnetic force provides the centripetal force

Part 6 of 7Applications and size of the effect

Applications and size of the effect

Cathode-ray tubes and mass spectrometers

Cathode-ray tubes and mass spectrometers a magnetic force bends beams of charged particles

Cosmic rays

Cosmic rays the Earth's field deflects them so that they spiral towards the poles, causing auroras

Velocity selector

Velocity selector crossed electric and magnetic fields pass only one speed (D.3.6)

Size

Size the force on an electron is tiny, but its mass of 9.11 × 10⁻³¹ kg makes the acceleration enormous

Sketching a path

Sketching a path draw the field with crosses or dots, mark the velocity and apply the rule for the sign of the charge to find the first small step

Part 7 of 7More from the specification

1Lorentz Force in Combined Fields

A charged particle moving through regions containing both a uniform electric field and a uniform magnetic field experiences electric force F_E = qE and magnetic Lorentz force F_B = qvB sin θ.

2Velocity Selector Condition

When electric and magnetic forces on moving ions are equal and opposite, particles with velocity v = E / B pass undeflected through parallel plates.
- (such as a proton or boron nucleus)

3Deflection and Charge-to-Mass Ratio

In a uniform magnetic field alone, charged particles undergo circular motion where radius r = mv / (qB);
- measuring trajectory curvature allows experimental determination of the specific charge or charge-to-mass ratio (q/m).

4Uniform

Same density throughout, so the weight acts at the centre.

5Proton

Positive particle in the nucleus, relative charge +1 and relative mass 1.

6Charge-to-mass ratio

Q/m, which determines the acceleration in a given field

7Field lines

Lines showing the direction and strength of a magnetic field.

8Field strength

G = F_g/m.

Key terms

Term	Meaning
Magnetic force on a charge	F = qvB sin θ on a moving charge in a magnetic field.
Elementary charge e	1.6 × 10⁻¹⁹ C, the size of the charge on a proton or electron.
Work done by a magnetic force	Zero, since the force is perpendicular to the velocity.
Hall effect	Sideways voltage across a conductor carrying current in a field.
Perpendicular component	The part of v at right angles to B; only it is deflected.

Avoid these mistakes

Saying a stationary charge feels a magnetic force — it does not.

Claiming the magnetic force increases the speed of the particle — it does no work, so speed is constant.

Using the same force direction for an electron as for a proton moving the same way — the force is reversed.

Forgetting sin θ for non-perpendicular motion.

Confusing the direction of v with the direction of conventional current for negative charges.

Last updated: 18 October 2026

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