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Magnetic force on moving charges (SACE Stage 2 Physics)

Syllabus dot point

“Calculate the magnetic force on a moving charge and determine its direction using the right-hand rule.”

9 min read

Quick answer

A magnetic field exerts a force on a charge only when the charge is moving across the field. The force is F=qvBsin⁡θF = qvB\sin\theta, where θ\theta is the angle between the velocity and the field. It is maximum when the motion is perpendicular to the field (θ=90∘\theta = 90^\circ) and zero when parallel. Its direction is perpendicular to both vv and BB, found with the right-hand rule.

Jump to a section
  1. What this dot point is asking
  2. Why the charge must be moving
  3. Direction: the right-hand rule
  4. Circular motion in a magnetic field
  5. Units
  6. How SACE assesses this
  7. Exam-style questions

What this dot point is asking

You need to calculate the magnetic force on a moving charge and determine its direction using a hand rule.

Force on a moving proton

A proton moves at 4.0×106 m s−14.0\times10^6\ \text{m s}^{-1} at right angles to a 0.50 T field

Find the magnetic force on it. Proton charge q=1.60×10−19 Cq = 1.60\times10^{-19}\ \text{C}.

Force (perpendicular, so sin⁡90∘=1\sin 90^\circ = 1):

F=qvB=(1.60×10−19)(4.0×106)(0.50)=3.2×10−13 N.F = qvB = (1.60\times10^{-19})(4.0\times10^6)(0.50) = 3.2\times10^{-13}\ \text{N}.

This force is perpendicular to both the proton's motion and the field, so it curves the proton into a circular arc without changing its speed.

Why the charge must be moving

A stationary charge in a magnetic field feels no magnetic force. Only when the charge moves does the field push on it, and only the component of velocity perpendicular to the field contributes.

Magnetic force on a moving charge

F=qvBsin⁡θF = qvB\sin\theta

FF is the force (N), qq the charge (C), vv its speed (m s−1\text{m s}^{-1}), BB the magnetic flux density (tesla, T), and θ\theta the angle between the velocity and the field. The force is greatest (F=qvBF = qvB) when θ=90∘\theta = 90^\circ and zero when the charge moves along the field (θ=0\theta = 0).

Direction: the right-hand rule

The force is perpendicular to both the velocity and the magnetic field; it cannot point along either. For a positive charge, point the fingers of your right hand along the velocity vv, curl them toward the field BB (or use the flat-hand "slap" rule: fingers along BB, thumb along vv, palm pushes in the force direction). The force is along your thumb/palm.

Hand rule and charge sign

Standard hand rules give the force direction for a positive charge. For a negative charge (such as an electron), the force is in the opposite direction. Always check the sign of the charge before quoting a direction.

Circular motion in a magnetic field

Because the magnetic force is always perpendicular to the velocity, it never changes the speed; it only changes direction. It does no work on the charge. A charge entering a uniform field perpendicular to it therefore moves in a circle, with the magnetic force providing the centripetal force (this is developed in the "charged particles in magnetic fields" dot point). If the charge enters at an angle, the velocity component along the field is unchanged and the path becomes a helix.

Units

The tesla is defined so that 1 T=1 N A−1m−11\ \text{T} = 1\ \text{N A}^{-1}\text{m}^{-1}, or equivalently 1 N1\ \text{N} per coulomb-metre-per-second. A 1 T field is strong; the Earth's field is around 5×10−5 T5\times10^{-5}\ \text{T}.

How SACE assesses this

SACE Stage 2 questions here split into a calculation type and an explanation type. The calculation gives a charge, speed and field and asks for the force using F=qvBsin⁡θF = qvB\sin\theta, usually with the velocity perpendicular to the field so sin⁡θ=1\sin\theta = 1. The explanation type asks why a charge entering a uniform field perpendicular to it undergoes uniform circular motion; the expected answer is that the force is always perpendicular to the velocity, so it does no work and changes only the direction (constant speed), making it a centripetal force. For the calculation, quote the formula, note the angle, and substitute in SI units; for the explanation, the two marking points are usually "force always perpendicular to velocity" and "acts as a centripetal force, giving uniform circular motion". Reverse the hand-rule direction for negative charges such as electrons.

Common errors
Forgetting motion is required
A stationary charge feels no magnetic force, and a charge moving parallel to the field (θ=0\theta = 0) also feels none.
Ignoring the charge sign
Hand rules give the direction for positive charges; reverse it for electrons and other negative charges.
Putting the force along vv or BB
The force is perpendicular to both; it can never point along the velocity or the field.
Thinking the field changes the speed
The magnetic force does no work; it changes direction only, so the speed (and kinetic energy) stays constant.

Exam-style questions

Questions in the style of SACE Board exam questions on this dot point, each with a worked answer. They are written by ExamExplained unless tagged "Past paper"; the year shows the paper a question is modelled on.

SACE 2025-style2 marks
A sigma particle of charge 1.60×10−19 C1.60\times10^{-19}\ \text{C} and speed 6.53×105 m s−16.53\times10^5\ \text{m s}^{-1} enters a uniform magnetic field of 0.172 T0.172\ \text{T} perpendicular to the field. Calculate the magnitude of the magnetic force on the particle as it enters the field.
Show worked answer →

The magnetic force is F=qvBsin⁡θF = qvB\sin\theta. The particle enters perpendicular to the field, so θ=90∘\theta = 90^\circ and sin⁡θ=1\sin\theta = 1.

F=qvB=(1.60×10−19)(6.53×105)(0.172)=1.80×10−14 N.F = qvB = (1.60\times10^{-19})(6.53\times10^5)(0.172) = 1.80\times10^{-14}\ \text{N}.

1 mark for F=qvBF = qvB, 1 mark for the answer of about 1.80×10−14 N1.80\times10^{-14}\ \text{N}. This force is the centripetal force that makes the particle follow a circular path.

SACE 2024-style2 marks
An electron undergoes uniform circular motion in a uniform magnetic field directed into the page, perpendicular to its velocity. Explain why the electron undergoes uniform circular motion in the field.
Show worked answer →

The magnetic force F=qvBsin⁡θF = qvB\sin\theta on the electron has a constant magnitude because the speed and the perpendicular field are constant.

The force always acts perpendicular to the velocity, so it does no work; the speed (and kinetic energy) stays constant.

A constant-magnitude force that is always perpendicular to the velocity is a centripetal force: it continually changes the direction of motion while keeping the speed constant, which is uniform circular motion. 1 mark for stating the force is always perpendicular to velocity (changing direction, not speed), 1 mark for identifying it as a centripetal force giving uniform circular motion.

Practise this

Sources & how we know this

Based on the official SACE Board subject outline. Not yet individually reviewed by a person; always check SACE Board and your school's materials for current rules.

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