Electromagnetic forces: currents, fields and beams
Key idea: Keep field production, conductor force and moving-charge force distinct, apply direction rules with charge sign, and compare electric and magnetic beam deflection before balancing crossed fields.
Before you start: Current Electricity objective chainD.C. Circuits objective chainElectric Fields objective chain
By the end, you can
- Represent and calculate magnetic fields produced by straight wires, flat coils and long solenoids.
- Analyse conductor forces, define flux density, use a current balance and predict parallel-current interactions.
- Calculate and direct magnetic force on moving positive or negative charges.
- Compare charged-beam deflection in uniform electric and magnetic fields.
- Explain and calculate crossed-field velocity selection.
Starting-point self-check
1. Check your starting point
Attempt all five groups without notes and mark the first geometry, direction, force, trajectory or balance decision you cannot justify. Use the recorded topic diagnostic above when you want scoring and a personalised repair plan.
Charged-particle beams in uniform fields 17(l)
Question 1
Compare the paths and energy changes of a positive beam entering uniform electric and magnetic fields perpendicular to its initial velocity.
Check the model response
The electric field gives constant force qE and can change speed and kinetic energy, producing a parabolic path while the field is uniform. The magnetic force qv × B stays perpendicular to velocity, does no work and gives circular motion when v is perpendicular to B.
repair
2. Repair the common breaks
Use only the correction matching an error, then retry the corresponding diagnostic.
Charged-particle beams in uniform fields 17(l)
Check this idea
Misconception: Magnetic force changes a particle's kinetic energy.
Repair: It is perpendicular to velocity and does no work; it changes direction, not speed.
Check this idea
Misconception: Electric and magnetic fields always produce the same path shape.
Repair: A uniform transverse E gives constant acceleration and a parabola; a uniform perpendicular B gives a circular arc.
worked example
3. Follow five worked models
Follow how each solution fixes source geometry, conventional direction, charge sign, field uniformity or force opposition before calculating.
Charged-particle beams in uniform fields 17(l)
Model 1
Derive the radius of a charged particle moving perpendicular to a uniform magnetic field.
Check the model response
The magnetic force supplies centripetal force: B|Q|v = mv²/r. Hence r = mv/(B|Q|). The force changes direction, not speed, so the path is circular while the field is uniform.
guided practice
4. Guided practice
Use each hint only to select the correct geometry, sine component, direction rule or force balance.
Charged-particle beams in uniform fields 17(l)
Question 1
A proton's speed doubles in the same perpendicular magnetic field. State the radius and period factors.
Hint: Derive each relationship rather than assuming both depend on speed.
Check the model response
r = mv/(BQ) doubles. T = 2πm/(BQ) is unchanged.
independent practice
5. Independent practice
Solve without repair notes and state every long-wire, flat-coil, long-solenoid, uniform-field and perpendicular-motion assumption.
Charged-particle beams in uniform fields 17(l)
Question 1
Analyse a charged beam entering a uniform electric field with transverse velocity, then a uniform magnetic field.
Check the model response
In E, constant qE gives constant transverse acceleration and a parabola while longitudinal velocity stays constant. In perpendicular B, qvB is centripetal, giving a circular arc of radius mv/(B|q|). Electric deflection can change speed; magnetic deflection cannot.
Practice exit check
6. Practice assessment
Use this as extra closed-book practice, then complete the separate recorded assessment in your plan.
Charged-particle beams in uniform fields 17(l)
Question 1
A proton with speed 3.0 × 10⁶ m s⁻¹ enters a 0.25 T field perpendicularly. Find its path radius using m = 1.67 × 10⁻²⁷ kg.
Check the model response
r = mv/(BQ) = (1.67 × 10⁻²⁷)(3.0 × 10⁶)/[(0.25)(1.60 × 10⁻¹⁹)] = 0.125 m.
Re-test practice
7. Delayed re-test practice
Return after at least three days and solve these fresh contexts without reopening earlier responses. The recorded plan enforces the delay and uses a separate re-test family for selected-response skill-group evidence.
Charged-particle beams in uniform fields 17(l)
Question 1
State why a magnetic field can bend a beam without changing its speed.
Check the model response
The magnetic force is perpendicular to velocity at every instant, so it changes momentum direction but does zero work and leaves kinetic energy and speed unchanged.