In simple terms
A friendly intro before the formal notes — no formulas yet.
Magnetic fields due to currents
Cambridge 9702 Paper 4 — Magnetic fields due to currents (20.4). Senpai Corner diagram-backed pilot with premium structure and live visuals.
- 1
A current-carrying wire produces a magnetic field consisting of concentric circles.
- 2
The direction of the field is given by the Right-Hand Grip Rule.
- 3
Field strength is directly proportional to the current ().
- 4
Field strength is inversely proportional to the perpendicular distance from the wire ().
What this topic covers
The official Cambridge syllabus points this lesson works through.
- 20.4.1
Sketch magnetic field patterns due to the currents in a long straight wire, a flat circular coil and a long solenoid
- 20.4.2
Understand that the magnetic field due to the current in a solenoid is increased by a ferrous core
- 20.4.3
Explain the origin of the forces between current-carrying conductors and determine the direction of the forces
Explore the concept
Use the live diagram, PhET or GeoGebra sim, and synced steps — play it, drag controls, or tap a step.
Step-synced diagram — highlights what to look for in the simulation above.
Moving charges create magnetic fields…
Moving charges create magnetic fields (current in a wire).
10 more simulations for this topic — run them in the Simulations section below
Simulations
Every simulation here runs the real model — try the steps on a card, then check what you see against the notes.
10 simulations · 5 to start with
Start herein this order — each one shows a different piece of the topic
- 3JCN PhysicsStart here · 19702 20.4 · 9702 20.1 · IB D.2
Magnetic Field Solenoid Mapping
Map the field inside and around a solenoid
Why this one: Map inside and around the solenoid: uniform parallel field inside, bar-magnet pattern outside.
Try this
- Map the field inside the solenoid.
- Map it outside and compare.
Look for Inside the field is strong and uniform; outside it resembles a bar magnet's.
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0
- 3JCN PhysicsStart here · 29702 20.4 · 9702 20.1 · IB D.2
Axial Magnetic Field inside Solenoid
Probe the axial field inside a solenoid; vary turns and current
Why this one: Change turns and current and see the axial field grow in proportion to nI.
Try this
- Probe the field along the axis and read B.
- Double the current and compare.
- Double the turns and compare.
Look for Inside a long solenoid B is uniform and proportional to current and turns per unit length.
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0
- 3JCN PhysicsStart here · 39702 20.4 · 9702 20.1 · IB D.2
Orsted's Compass
Switch on a current and see a compass deflect, as Oersted did
Why this one: Switch on a current and watch the compass deflect — the wire's field wraps around it.
Try this
- Switch on the current and watch the compass.
- Reverse the current and compare.
Look for A current produces a magnetic field, and reversing the current reverses the compass deflection.
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0
- 3JCN PhysicsStart here · 49702 20.2 · 9702 20.4 · IB D.3
Forces on current-carrying wires
Run parallel currents in two wires; see attraction or repulsion
Why this one: Each wire sits in the other's field: parallel currents attract, antiparallel repel.
Try this
- Run the two currents in the same direction and watch the wires.
- Reverse one current and compare.
Look for Parallel currents attract and antiparallel currents repel.
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0
- SimuPhysicsStart here · 59702 20.4 · IB D.2
Field due to a Straight Wire
Field lines are plotted around a straight wire; probe the strength at any distance
Why this one: Probe the concentric field around a straight wire and see it weaken as you move away.
Try this
- Probe the field close to the wire.
- Double the distance and probe again.
- Reverse the current.
Look for Field strength is inversely proportional to distance from the wire.
Open on SimuPhysicsRuns on their siteSimuPhysics by Mohamed Abdelsalam · Licensed to MarkScheme (site publishes no licence; served with frame-ancestors self)
More simulations5 more on this topic — core ones first
- The Physics ClassroomCore9702 20.4 · IB D.2
Electromagnet
Build an electromagnet and explore what increases the strength of its magnetic field
Try this
- Add turns to the coil.
- Increase the current.
- Add an iron core.
Look for Field strength grows with the current and the number of turns.
Physics Interactives by The Physics Classroom · Licensed to MarkScheme (site terms otherwise permit linking only)
- SimuPhysicsCore9702 20.4 · IB D.2
Circular Coil into a Solenoid 3D
A solenoid is built one circular loop at a time in 3D so you can watch the field evolve
Try this
- Start with one loop and look at its field.
- Add loops and watch the field merge.
- Compare the interior field of the full solenoid.
Look for Stacking loops produces a uniform field inside the solenoid.
Open on SimuPhysicsRuns on their siteSimuPhysics by Mohamed Abdelsalam · Licensed to MarkScheme (site publishes no licence; served with frame-ancestors self)
- SimuPhysicsCore9702 20.4 · 9702 20.1 · IB D.2
Compass Above and Below Wire
Compasses sit above and below a current-carrying wire; they point in opposite directions because the field wraps round the wire
Try this
- Switch the current on and watch both compasses.
- Reverse the current.
- Compare the two compass directions.
Look for The field circles the wire, so compasses above and below point in opposite directions.
Open on SimuPhysicsRuns on their siteSimuPhysics by Mohamed Abdelsalam · Licensed to MarkScheme (site publishes no licence; served with frame-ancestors self)
- SimuPhysicsCore9702 20.4 · IB D.2
Neutral Point Between Two Parallel Wires
Two parallel wires each produce a circular field; find the neutral point and see how it shifts when the currents change
Try this
- Set equal currents and find the neutral point.
- Double one current and find it again.
- Reverse one current.
Look for The neutral point lies closer to the wire carrying the smaller current.
Open on SimuPhysicsRuns on their siteSimuPhysics by Mohamed Abdelsalam · Licensed to MarkScheme (site publishes no licence; served with frame-ancestors self)
- 3JCN Physics9702 20.4 · IB D.2
Electric Bell - Electromagnet
Operate an electric bell driven by an electromagnet
Try this
- Press the switch and watch the electromagnet pull the hammer.
- Follow how the contact breaks and the hammer springs back.
Look for The electromagnet switches itself off when the hammer moves, so the hammer vibrates.
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0
Key formulas
Tap any symbol to reveal exactly what it means and its units.
Tap a symbol — great for exam definitions
Tap a symbol — great for exam definitions
Tap a symbol — great for exam definitions
Full topic notes
Formal explanation with the rigour you need for the exam.
Magnetic Fields from Straight Wires
When an electric current flows through a straight conductor, it generates a magnetic field in the space around it. This field isn't random; its pattern forms distinct concentric circles that encircle the wire. The field strength is strongest closest to the wire and diminishes as you move further away. The specific direction of these circular magnetic field lines is crucial and can be found using a simple hand rule.
The Right-Hand Grip Rule is your key to understanding field direction. Imagine grasping the wire with your right hand: if your thumb points in the direction of the conventional current (positive to negative), then your curled fingers will indicate the direction of the magnetic field lines around the wire. This rule is essential for correctly interpreting magnetic phenomena.
The strength of this magnetic field (B), also known as magnetic flux density, at a perpendicular distance 'r' from a long straight wire is given by: Here, I is the current, and is the permeability of free space (), a constant describing how magnetic fields interact with a vacuum.
A current-carrying wire produces a magnetic field consisting of concentric circles.
The direction of the field is given by the Right-Hand Grip Rule.
Field strength is directly proportional to the current ().
Field strength is inversely proportional to the perpendicular distance from the wire ().
Forces Between Parallel Current-Carrying Wires
Because each current-carrying wire produces its own magnetic field, two parallel wires carrying currents will exert magnetic forces on each other. This interaction is a direct consequence of one wire's current experiencing a force from the other wire's magnetic field (as per ). The direction of this force depends entirely on the relative directions of the currents.
The force per unit length () between two long, parallel current-carrying wires separated by a distance 'r' is: Where and are the currents in the two wires.
Two parallel current-carrying wires exert equal and opposite forces on each other.
If currents flow in the same direction, the wires attract.
If currents flow in opposite directions, the wires repel.
Magnetic Fields from Coils and Solenoids
A single loop of current-carrying wire also generates a magnetic field, most intense at its centre. However, for a powerful and controlled magnetic field, we turn to solenoids. A solenoid is essentially a long coil of wire, tightly wound, which produces a remarkably strong and uniform magnetic field within its interior when current flows through it. This makes them powerful and controllable electromagnets.
The magnetic flux density B inside a long solenoid (far from its ends) is given by: where is the current and is the number of turns per unit length (, where N is total turns and L is length).
The ability to create a strong, uniform magnetic field that can be switched on and off makes solenoids incredibly useful. They are the core component of electromagnets, which are used in a vast range of applications, including electric relays, circuit breakers, MRI machines, and particle accelerators.
A solenoid is a coil of wire that produces a strong, uniform magnetic field inside when current flows.
The external field pattern of a solenoid resembles that of a bar magnet.
The polarity (N/S poles) is found using the Right-Hand Grip Rule: fingers follow the current, thumb points to North.
Clockwise current (viewed from an end) means that end is a South pole.
Anti-clockwise current (viewed from an end) means that end is a North pole.
Adding a soft iron core (making an electromagnet) greatly increases the field strength.
Always remember to apply the Right-Hand Grip Rule consistently for both straight wires and solenoids (to determine polarity). Double-check the direction of current for parallel wires; 'same direction' means attraction, 'opposite direction' means repulsion – this is a common point for losing marks if confused!
Worked examples
See the formulas applied — reveal one step at a time, like the exam.
A long, straight electrical cable carries a steady current of 12.0 A. Calculate the magnetic flux density at a point 4.0 cm from the centre of the cable. (Use )
- 1
Identify known values and convert units:
Two long, parallel wires are separated by a distance of 0.15 m. Wire 1 carries a current of 3.0 A, and Wire 2 carries a current of 5.0 A in the same direction. Calculate the force per unit length between the wires. ()
- 1
Identify known values:
How it all connects
The big idea sits in the middle — tap a linked idea to explore the link.
Tap a linked idea to see how it connects back to the main topic — that connection is what examiners reward.
Glossary
Key terms for this topic — skim now; the Check step will test them.
- Right-Hand Grip Rule
The Right-Hand Grip Rule is your key to understanding field direction.
- conventional current
If your thumb points in the direction of the conventional current (positive to negative), then your curled fingers will indicate the direction of the magnetic field lines around the wire.
- magnetic field lines
Imagine grasping the wire with your right hand: if your thumb points in the direction of the conventional current (positive to negative), then your curled fingers will indicate the direction of the magnetic field lines around the wire. This rule is essential for correctly interpreting magnetic phenomena.
- electromagnets
They are the core component of electromagnets, which are used in a vast range of applications, including electric relays, circuit breakers, MRI machines, and particle accelerators.
- permeability of free space
The strength of this magnetic field (B), also known as magnetic flux density, at a perpendicular distance 'r' from a long straight wire is given by: Here, I is the current, and is the permeability of free space (), a constant describing how magnetic fields interact with a vacuum.
Quick check
Write your answer first, then compare it with the model one — the gap is what you would have lost.
Teach it back
If you can explain it simply, you own it — gaps here are marks you’d lose.
Teach it back
Explain this topic as if teaching a friend. We name the gaps an examiner would still dock.
Revision flashcards
Guess first, then flip — retrieval beats re-reading.
Key takeaways
Review these before you close the topic — retrieval beats re-reading.
A current-carrying wire produces a magnetic field consisting of concentric circles.
The direction of the field is given by the Right-Hand Grip Rule.
Field strength is directly proportional to the current ().
Field strength is inversely proportional to the perpendicular distance from the wire ().
Practice — then mark it
The whole point: a real Cambridge question, marked mark-by-mark.
Explain why the two wires exert a magnetic force on each other.
On Fig. 7.1, draw four field lines to represent the magnetic field around the wire due to the current in it.
Extra simulations & links
PhET, GeoGebra and other curated tools — open in a new tab.
Frequently asked
Checkpoint
One marked question is worth ten re-reads — close the loop before you move on.
Reading it isn’t knowing it — prove it.
Before you move on: do 9702/41 · Q7(c)(i) on paper, snap a photo, and get examiner-style feedback on exactly where you win and lose marks.
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