Key Idea: This topic is about the forces that electric and magnetic fields put on charges — and the motion those forces cause. Three set-ups recur: a current-carrying wire pushed by a magnetic field (the motor effect), a charge in an electric field accelerated like a projectile, and a moving charge in a magnetic field bent into a circle, used in the velocity selector. It is examined on both papers. Paper 1A is quick multiple-choice — the direction of a force from a left-hand rule, when the force is zero, what path a particle follows, whether the selected speed depends on the charge. Paper 2 is longer structured work — find a field strength from F = BIL, a two-step F = qE then a = F/m calculation, a 'show that' on a huge acceleration, a projectile-style deflection with s = ½at², or a crossed-fields balance qE = qvB.
📋 Key formulas
Most of these carry the data-booklet badge (look for it). The selector speed v = E/B and the circular-path radius r = mv/(qB) are not printed separately — they come straight from balancing or equating the given forces, so you remember those.
- force on the wire (N)
- magnetic field strength / flux density (T, tesla)
- current in the wire (A)
- length of wire in the field (m)
- angle between the current and the magnetic field
- electric force on the charge (N)
- the charge in the field (C, coulombs)
- electric field strength (N C⁻¹, or V m⁻¹)
- net (electric) force on the charge (N)
- mass of the charged particle (kg)
- acceleration of the particle (m s⁻²)
- electric field strength between the plates (V m⁻¹, or N C⁻¹)
- potential difference (voltage) between the plates (V)
- separation (gap) between the plates (m)
- magnetic force on the moving charge (N)
- size of the moving charge (C)
- speed of the charge (m s⁻¹)
- magnetic field strength (T, tesla)
- radius of the circular path (m)
- mass of the charged particle (kg)
- speed of the particle (m s⁻¹)
- size of the charge (C)
- magnetic field strength (T)
- selected speed — the speed that passes straight through (m s⁻¹)
- electric field strength between the plates (N C⁻¹ or V m⁻¹)
- magnetic field strength (T)
⚖️ The three force set-ups side by side
| Set-up | What feels the force | Key relationship | What to remember |
|---|---|---|---|
| Current in a magnetic field (motor effect) | A current-carrying wire | F = BIL sinθ | Direction from Fleming's left-hand rule (First finger Field, seCond finger Current, thuMb Force). Force is zero when the current runs along the field (θ = 0). |
| Charge in an electric field | Any charge, moving or not | F = qE, then a = F/m | Two steps every time. A positive charge accelerates along the field, a negative one (electron) opposite it. Fired across → parabola. |
| Moving charge in a magnetic field | Only a MOVING charge (need v) | F = qvB; r = mv/(qB) | Force is perpendicular to v, so it changes direction only, never speed — a circular path. A stationary charge feels no magnetic force. |
| Velocity selector (crossed E and B) | A moving charge in both fields | qE = qvB → v = E/B | Only the speed where the two forces balance passes straight through. The selected speed v = E ÷ B is the same for every charge — q cancels. |
🧲 Electric force vs magnetic force on a charge
| Electric force | Magnetic force | |
|---|---|---|
| Size | F = qE | F = qvB (at right angles to B) |
| Needs the charge to move? | No — acts even on a charge at rest | Yes — zero unless the charge is moving (v = 0 → F = 0) |
| Direction | Along the field (opposite for a − charge) | Perpendicular to BOTH v and B (always sideways) |
| Effect on the motion | Changes the speed — can speed up or slow the charge | Changes the direction only — does no work, so speed/KE stays constant |
| Path it produces | Straight-line acceleration, or a parabola if fired across | A circle, radius r = mv/(qB) |
Force on a wire → Fleming's left-hand rule: First finger Field, seCond finger Current, thuMb Force (Motion). Reverse the current OR the field and the force flips. Force on a charge → for a positive charge it follows the field directions above; for a negative charge (an electron) every force is the opposite way.
✏️ Worked exam-style questions
A straight wire of length 0.20 m lies at right angles to a uniform magnetic field and carries a current of 5.0 A. (a) The field strength is 0.30 T — find the force on the wire. (b) In a second experiment the same wire (same length, same 5.0 A current) feels a force of 0.45 N. Find the new field strength B.
🔒 Model answer plan
See the mark-by-mark plan — for / against / judgement, with marking guidance — in study mode.
An electron (charge 1.6 × 10⁻¹⁹ C, mass 9.1 × 10⁻³¹ kg) sits in the uniform field between two parallel plates 0.025 m apart with 250 V across them. (a) Find the field strength E. (b) Find the electric force on the electron. (c) Show that its acceleration is of order 10¹⁵ m s⁻², and state its direction relative to the field.
🔒 Model answer plan
See the mark-by-mark plan — for / against / judgement, with marking guidance — in study mode.
An electron enters the gap between two parallel plates moving parallel to them at 5.0 × 10⁷ m s⁻¹. The plates are 0.060 m long and the field gives the electron a sideways acceleration of 3.2 × 10¹⁴ m s⁻². (a) Find the time the electron spends between the plates. (b) Find how far it is deflected sideways as it crosses, and explain why s = ½at² is used rather than s = vt.
🔒 Model answer plan
See the mark-by-mark plan — for / against / judgement, with marking guidance — in study mode.
An ion of charge 1.6 × 10⁻¹⁹ C and mass 2.5 × 10⁻²⁶ kg passes undeflected through a velocity selector whose crossed fields are E = 3.6 × 10⁴ N C⁻¹ and B₁ = 0.18 T. After the selector the ion enters a region of magnetic field B₂ = 0.40 T alone, at right angles to its motion. (a) Find the selected speed. (b) Find the radius of the circular path the ion then follows.
🔒 Model answer plan
See the mark-by-mark plan — for / against / judgement, with marking guidance — in study mode.
🧠 Quick self-check
Tap each card to reveal the answer.
A current runs ALONG (parallel to) a magnetic field — what force does the wire feel? None. With θ = 0, sin 0 = 0, so F = BIL sinθ = 0. The force is largest when the current is at right angles to the field (θ = 90°).
Which hand and which fingers give the direction of the force on a wire? Fleming's left hand: First finger = Field, seCond finger = Current, thuMb = force / Motion.
How do you get a charged particle's acceleration in an electric field? Two steps: force F = qE first, then Newton's second law a = F ÷ m = qE ÷ m. A light particle (electron) gets a huge acceleration.
What path does a charge fired ACROSS a uniform field follow, and which equation gives the deflection? A parabola, like a projectile — constant velocity along the plates, constant acceleration across them. The sideways shift is s = ½at² (not s = vt).
Why does a magnetic field bend a charge into a circle without changing its speed? F = qvB is always perpendicular to v, so it does no work — the kinetic energy (and speed) stays constant while the direction keeps changing, giving a circle of radius r = mv/(qB).
Does the speed selected by a velocity selector depend on the charge? No. Balancing qE = qvB cancels q, so v = E ÷ B is the same for every particle, whatever its charge or mass.
🎯 Exam tips
Exam Tips
- Force on a wire: use F = BIL sinθ; set sinθ = 1 when the wire is at right angles to the field, and remember the force is ZERO when the current runs along the field. F is proportional to both B and I, so doubling either doubles the force.
- Direction of the force on a wire = Fleming's LEFT-hand rule: First finger Field, seCond finger Current, thuMb Force. Reverse the current or the field and the force flips.
- Charge in an electric field is ALWAYS two steps: F = qE first, then a = F ÷ m. Don't read the field strength E as the acceleration. A positive charge accelerates along the field; an electron accelerates opposite to it.
- Use E = V/d to turn a plate voltage into a field, then F = qE for the force. Watch the units — convert a plate gap in cm or mm to metres before dividing.
- Fired across the field = a projectile: constant velocity along the plates (gives the time), s = ½at² across them (gives the deflection). Never use s = vt for the accelerated sideways direction.
- A magnetic force F = qvB acts only on a MOVING charge and is perpendicular to v, so it does no work — it bends the path into a circle of radius r = mv/(qB) but never changes the speed.
- Velocity selector: balance qE = qvB → v = E ÷ B. The charge cancels, so the selected speed is the same for any particle. Too slow → the electric force wins; too fast → the magnetic force wins.