Magnetic fields produced by currents
Key idea: H2 Physics lessons on current-produced fields, magnetic forces and crossed-field velocity selection.
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The core idea
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Big question: How does current shape the magnetic field around a conductor?
Conventional current produces circular field lines around a straight wire, a bar-magnet-like field around a flat coil and a nearly uniform field inside a long solenoid. Use the right-hand grip rule for direction and the equation matching the conductor geometry. A ferrous core can greatly strengthen a solenoid's field.
Draw each current-produced field
A magnetic field is produced by permanent magnets and by electric currents. Around a long straight wire, field lines are concentric circles. Point the right thumb with conventional current and the curled fingers give B direction.
A flat circular coil has a bar-magnet-like pattern through its centre. A long solenoid has a nearly uniform internal field and a much weaker external return field. Reversing current reverses every field arrow and swaps the solenoid's magnetic poles.
Check your understanding: What changes when solenoid current reverses?
Its field direction and north–south ends reverse; the pattern shape remains the same.
Choose the field-strength equation from the geometry
At distance d from a long straight wire, B = μ₀I/(2πd). At the centre of a flat circular N-turn coil of radius r, B = μ₀NI/(2r). Inside a long solenoid, B = μ₀nI, where n is turns per unit length, not total turns.
A ferrous core can greatly increase a solenoid's magnetic flux density because the material becomes magnetised. State the core condition rather than treating μ₀nI as unchanged when a core is inserted.
Check your understanding: Which quantity belongs in the long-solenoid equation: N or n?
Use n, the number of turns per unit length.
Key ideas to keep
- Do not confuse total turns N with turns per unit length n.
- Reverse current and the field direction reverses.
- Closer lines indicate stronger field but are not physical threads.
See the reasoning
Worked example
Compare a flat coil with a long solenoid
Question: 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.
Step 1: Choose the coil expression
Why: A flat circular coil uses total turns N and radius r.
Working: Bcoil = μ₀NI/(2r) = 2.36×10⁻⁴ T.
Step 2: Choose the solenoid expression
Why: A long solenoid uses turns per unit length n.
Working: Bsolenoid = μ₀nI = 2.26×10⁻³ T.
Step 3: Compare like quantities
Why: Both values are flux densities in tesla at the stated regions.
Working: The solenoid field is about 9.6 times larger.
Answer: 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.
Check: Do not substitute total turns into the solenoid's turns-per-metre symbol.
Use a hint if needed
Practise with support
Try this
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 your answer
B = μ₀nI doubles. A ferrous core magnetises and reinforces the field, increasing B beyond the air-core value.
Now work without the hint
Practise independently
Your turn
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 your answer
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.
Avoid these traps
Common mistakes
Common mistake
All current-produced fields use the same distance formula.
What is wrong with this reasoning?
Show better thinking
Use the equation for the named geometry: long wire, flat circular coil or long solenoid.
Common mistake
A ferrous core leaves the solenoid field unchanged.
What is wrong with this reasoning?
Show better thinking
The core magnetises and can substantially reinforce the field, so the air-core expression is no longer the whole model.
Write for the examiner
Exam guidance
Draw current direction before applying the grip rule, and add fields vectorially where patterns overlap.
Exam-style practice [5 marks]
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.
Plan before you answer
- Use the centre-of-coil equation.
- Keep radius in metres.
- Apply the grip rule after calculating magnitude.
Mark your answer and compare the model
Marking points
Tick each point only if your answer states it clearly.
Model answer
B = μ₀NI/(2r) = 2.51 × 10⁻⁴ T. Reversing current reverses field direction without changing magnitude.
Come back in three days
Check what stayed with you
Recall question
At fixed current, distance from a long wire triples. State the field factor.
Check the answer
B = μ₀I/(2πd), so it becomes one third.
Syllabus and review details
This lesson covers the listed H2 Physics 9478 outcomes. Topic 17 states no explicit exclusions. Straight-wire, flat-coil and long-solenoid field equations use their named ideal geometries; a ferrous core changes the air-core model. In F = BIl sin θ, θ is between conventional current and B; in F = BQv sin θ, direction is determined for positive charge then reversed for negative charge. Magnetic force does no work. Circular-path formulae require velocity perpendicular to a uniform B. Velocity selection requires uniform mutually perpendicular E, B and beam velocity with opposing forces.
- GCE A-Level H2 PhysicsTopic 17(a) / Topic 17(b) / Topic 17(c) / Topic 17(d) · 2027Checked against the syllabus · partial topic coverageOfficial 9478 syllabus
Course and syllabus information
- Course
- GCE A-Level H2 Physics
- Edition
- GCE A-Level H2 Physics 2027