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.
Magnetic fields produced by currents 17(a)–(d)
Question 1
State the field direction and calculate B at 3.0 cm from a long straight wire carrying 8.0 A. Use μ₀ = 4π × 10⁻⁷ H m⁻¹.
Check the model response
Field lines are concentric circles with direction from the right-hand grip rule. B = μ₀I/(2πd) = 5.33 × 10⁻⁵ T.
repair
2. Repair the common breaks
Use only the correction matching an error, then retry the corresponding diagnostic.
Magnetic fields produced by currents 17(a)–(d)
Check this idea
Misconception: All current-produced fields use the same distance formula.
Repair: Use the equation for the named geometry: long wire, flat circular coil or long solenoid.
Check this idea
Misconception: A ferrous core leaves the solenoid field unchanged.
Repair: The core magnetises and can substantially reinforce the field, so the air-core expression is no longer the whole model.
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.
Magnetic fields produced by currents 17(a)–(d)
Model 1
Compare B at the centre of a 20-turn flat circular coil of radius 0.080 m carrying 1.5 A with B inside a long solenoid of 1200 turns m⁻¹ carrying the same current.
Check the model response
Coil: B = μ₀NI/(2r) = 2.36 × 10⁻⁴ T. Solenoid: B = μ₀nI = 2.26 × 10⁻³ T. The expressions use total turns N for the coil and turns per unit length n for the solenoid.
guided practice
4. Guided practice
Use each hint only to select the correct geometry, sine component, direction rule or force balance.
Magnetic fields produced by currents 17(a)–(d)
Question 1
Current in a long solenoid doubles while n stays fixed. State the field factor and effect of a ferrous core.
Hint: Separate the equation's current change from the material effect.
Check the model response
B = μ₀nI doubles. A ferrous core magnetises and reinforces the field, increasing B beyond the air-core value.
independent practice
5. Independent practice
Solve without repair notes and state every long-wire, flat-coil, long-solenoid, uniform-field and perpendicular-motion assumption.
Magnetic fields produced by currents 17(a)–(d)
Question 1
Sketch verbally the field patterns for a long straight wire, flat circular coil and long solenoid, and distinguish N from n in their equations.
Check the model response
A wire has concentric circular lines. A coil has a bar-magnet-like pattern through its centre. A long solenoid has nearly uniform parallel internal lines with return lines outside. The coil formula uses total turns N; the solenoid formula uses turns per unit length n.
Practice exit check
6. Practice assessment
Use this as extra closed-book practice, then complete the separate recorded assessment in your plan.
Magnetic fields produced by currents 17(a)–(d)
Question 1
Calculate B at the centre of a 50-turn coil of radius 0.10 m carrying 0.80 A, then state the effect of reversing current.
Check the model response
B = μ₀NI/(2r) = 2.51 × 10⁻⁴ T. Reversing current reverses field direction without changing magnitude.
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.
Magnetic fields produced by currents 17(a)–(d)
Question 1
At fixed current, distance from a long wire triples. State the field factor.
Check the model response
B = μ₀I/(2πd), so it becomes one third.