Short on time? This page is the recap. For explanations, Figures 1 and 2 and the worked examples, use the full study guide.
Recap
- A moving charge makes a magnetic field. At a point, B is at right angles to both v and the line from the charge to the point. It is stronger for faster charges and closer points, largest when v ⟂ r, and zero straight ahead or behind.
- Magnetic forces are interactions between moving charges: one makes the field, the other feels it.
- A field pushes on a moving charge with a force at right angles to both v and B.
- Right-hand rule: fingers along v, curl towards B, thumb = force on a positive charge. Reverse it for a negative charge.
- The force does no work. A charge moving at right angles to a uniform field goes round a circle at constant speed.
- With E and B both present, the two forces act independently; add them as vectors.
- Hall effect: carriers pushed to one edge of a conductor create a potential difference across it.
Key relationships
| Relationship | Conditions and units | Use it to |
|---|---|---|
| F_B = qvB sin θ | q = size of the charge in C, v in m/s, B in T; calculate at θ = 0°, 90°, 180° only | find the size of the magnetic force |
| r = mv/(qB) | v ⟂ B, uniform field | find the radius of the circular path |
| T = 2πm/(qB) | v ⟂ B | find the time for one orbit (independent of speed) |
| v = E/B | crossed fields, forces opposite | find the speed that passes undeflected |
| ΔV_H = vBw | v = drift speed, w = width, B ⟂ current | relate Hall voltage, drift speed and field |
Symbols: × = field into the page; · = field out of the page.
Assumptions behind the numbers
- Fields are uniform and steady in the region.
- Gravity on particles such as protons and electrons is ignored: it is far smaller than the electric and magnetic forces here.
- In the Hall effect, the carriers have reached a steady state, so the sideways forces balance.
Mistakes to avoid
- Forgetting to reverse the right-hand rule for electrons.
- Saying the magnetic force changes a charge’s speed.
- Giving a non-zero force when v is parallel or antiparallel to B.
- Drawing the field of a moving charge along its velocity.
- Thinking a velocity selector picks out a particular charge or mass.
- Writing “because of the right-hand rule” with no directions stated.
Quick self-check
- An electron moves to the right through a field out of the page. Which way is the force? (Positive charge: down the page; electron: up the page.)
- A particle’s speed is tripled in the same field. By what factor does the radius of its circle change? (×3)
- Plates give E = 4.0 × 10⁴ V/m and the crossed field is 0.20 T. Which speed passes straight through? (2.0 × 10⁵ m/s)
Next: practice questions.