In simple terms
A friendly intro before the formal notes — no formulas yet.
Force on a current-carrying conductor
Cambridge 9702 Paper 4 — Force on a current-carrying conductor (20.2). Senpai Corner diagram-backed pilot with premium structure and live visuals.
- 1
20.2 Force on a current-carrying conductor.
- 2
A current carrying conductor produces its own magnetic field.
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When interacting with an external magnetic field, it will experience a force.
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A current-carrying conductor will only experience a force if the current through it is perpendicular to the direction of the magnetic field lines.
What this topic covers
The official Cambridge syllabus points this lesson works through.
- 20.2.1
Understand that a force might act on a current-carrying conductor placed in a magnetic field
- 20.2.2
Recall and use the equation , with directions as interpreted by Fleming's left-hand rule
- 20.2.3
Define magnetic flux density as the force acting per unit current per unit length on a wire placed at right-angles to the magnetic field
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.
Step 1
20.2 Force on a current-carrying conductor.
12 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.
12 simulations · 5 to start with
Start herein this order — each one shows a different piece of the topic
- The Physics ClassroomStart here · 19702 20.2 · IB D.3
Magnetic Field Sim (Kirby)
Adjust the current, conductor length, field strength and orientation and see the force on the wire
Why this one: Change the current, wire length, field and orientation and check the force direction with Fleming's left hand.
Try this
- Double the current and read the force.
- Rotate the wire parallel to the field.
- Double the conductor length.
Look for The force equals BIL sin θ.
Physics Interactives by The Physics Classroom · Licensed to MarkScheme (site terms otherwise permit linking only)
- oPhysicsStart here · 29702 20.2 · IB D.3 · IB D.2
DC Motor
DC motor: adjust voltage, field strength and number of turns; see force on the coil and rotation
Why this one: Watch the two sides of the coil feel opposite forces — a couple that turns the coil.
Try this
- Increase the voltage and watch the rotation.
- Reverse the field.
- Add turns to the coil.
Look for The force on each side of the coil grows with current, field and turns, and reversing the field reverses the rotation.
Simulation by Tom Walsh, oPhysics.com — made with GeoGebra · Licensed to MarkScheme (site: free for non-profit educational use; applets made with GeoGebra)
- 3JCN PhysicsStart here · 39702 20.2 · IB D.3
DC Motor
Run a DC motor; see the force couple and commutator reversal
Why this one: Follow the commutator reversing the current every half turn so the coil keeps turning one way.
Try this
- Run the motor and watch the forces on the two sides of the coil.
- Watch the commutator reverse the current each half turn.
Look for Opposite forces on the two sides make a couple, and the commutator keeps the torque in one direction.
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: Run two parallel currents: same direction attracts, opposite repels.
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 20.2 · IB D.3
3D Fleming's Left Hand Rule
Rotate a hand model in 3D together with the field, current and force vectors until the rule makes sense
Why this one: Rotate the hand model with the field, current and force vectors until the rule makes sense in 3D.
Try this
- Rotate the hand so the first finger lies along the field.
- Line the second finger up with the current.
- Read the force direction from the thumb.
Look for Field, current and force are mutually perpendicular.
Open on SimuPhysicsRuns on their siteSimuPhysics by Mohamed Abdelsalam · Licensed to MarkScheme (site publishes no licence; served with frame-ancestors self)
More simulations7 more on this topic — core ones first
- SimuPhysicsCore9702 20.2 · IB D.3
Force on a Straight Wire
A current-carrying wire in a magnetic field; vary the angle between current and field and watch the force vector
Try this
- Set the angle to 90° and read the force.
- Reduce the angle and compare.
- Set the wire parallel to the field.
Look for The force equals BIL sin θ and is zero when the wire is parallel to the field.
Open on SimuPhysicsRuns on their siteSimuPhysics by Mohamed Abdelsalam · Licensed to MarkScheme (site publishes no licence; served with frame-ancestors self)
- SimuPhysicsCore9702 20.2 · IB D.3
Torque on a Current-Carrying Rectangular Coil
The forces on each side of a rectangular coil in a uniform field are isolated in 3D; rotate the coil while watching the arrows
Try this
- Rotate the coil and watch the force arrows.
- Find where the torque is largest.
- Find where it is zero.
Look for Torque is greatest with the coil plane parallel to the field and zero when perpendicular.
Open on SimuPhysicsRuns on their siteSimuPhysics by Mohamed Abdelsalam · Licensed to MarkScheme (site publishes no licence; served with frame-ancestors self)
- SimuPhysics9702 20.2 · IB D.3
3D Galvanometer
A moving-coil galvanometer in 3D: rotate the view to see the coil in the field of the curved pole pieces and watch the pointer settle
Try this
- Rotate the view to see the coil and pole pieces.
- Pass a current and watch the torque develop.
- Watch the pointer settle.
Look for The pointer settles where the magnetic torque balances the spring torque.
Open on SimuPhysicsRuns on their siteSimuPhysics by Mohamed Abdelsalam · Licensed to MarkScheme (site publishes no licence; served with frame-ancestors self)
- SimuPhysics9702 20.2 · IB D.3
3D Galvanometer 2
Explore the coil, magnet and spring in 3D and see how the motor effect turns a current of a few microamps into a deflection
Try this
- Rotate the view to see the coil, magnet and spring.
- Pass a small current and read the scale.
- Double the current and compare.
Look for Deflection is proportional to current.
Open on SimuPhysicsRuns on their siteSimuPhysics by Mohamed Abdelsalam · Licensed to MarkScheme (site publishes no licence; served with frame-ancestors self)
- SimuPhysics9702 20.2 · IB D.3
DC Motor
Follow the current path through the coil, the forces on each side, and the moment the split ring reverses the connection
Try this
- Watch the forces on each side of the coil.
- Watch the split ring at the vertical position.
- Reverse the current.
Look for The split-ring commutator reverses the current every half turn so the torque keeps the same sense.
Open on SimuPhysicsRuns on their siteSimuPhysics by Mohamed Abdelsalam · Licensed to MarkScheme (site publishes no licence; served with frame-ancestors self)
- SimuPhysics9702 20.2 · IB D.3
DC Motor - Multiple Coils
Add coils around the armature and compare the torque trace with the single-coil version
Try this
- Run the single coil and read the torque trace.
- Add coils and compare.
- Find the dead points.
Look for More coils give a smoother torque with no dead points.
Open on SimuPhysicsRuns on their siteSimuPhysics by Mohamed Abdelsalam · Licensed to MarkScheme (site publishes no licence; served with frame-ancestors self)
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
Full topic notes
Formal explanation with the rigour you need for the exam.
The Motor Effect: Force on a Conductor
When an electric current flows through a wire, it creates its own magnetic field. If this wire is then placed inside another external magnetic field, these two fields interact. This interaction results in a push or pull, a force, on the wire. This is the motor effect, and it's how electrical energy can be converted into mechanical motion.
Magnetic Flux Density (B)
To quantify the strength of a magnetic field, we use magnetic flux density, denoted by 'B'. Think of it as how 'dense' the magnetic field lines are, and thus, how strong the field's influence is.
20.2 Force on a current-carrying conductor.
A current carrying conductor produces its own magnetic field.
When interacting with an external magnetic field, it will experience a force.
A current-carrying conductor will only experience a force if the current through it is perpendicular to the direction of the magnetic field lines.
Magnetic field strength is measured in magnetic flux density (B).
The units for B are in Tesla .
Calculating the Force: The F = BILsinθ Formula
The magnitude of the force (F) experienced by a current-carrying conductor in a magnetic field depends on several factors. It's not just about the strength of the field, but also how much current is flowing, the length of the wire within the field, and crucially, the angle at which the current crosses the magnetic field lines.
F = BILsinθ
F: Force on the conductor (in Newtons, N).
B: Magnetic flux density (in Tesla, T).
I: Current in the conductor (in Amperes, A).
L: Length of the conductor within the magnetic field (in meters, m).
θ: Angle between the direction of the current and the magnetic field lines.
Remember to use the length of the conductor within the magnetic field (L), not necessarily the total length of the wire. Often, only a specific section of a circuit might be in the field, so identify that 'L' carefully.
When is the Force Maximum or Zero?
The sinθ term in our force formula, F = BILsinθ, is crucial for understanding how the angle affects the force. The sine function varies from 0 to 1, meaning the force can change dramatically based on the wire's orientation.
Maximum Force (F = BIL): Occurs when the current is perpendicular to the magnetic field lines (θ = 90°), as sin(90°) = 1.
Zero Force (F = 0): Occurs when the current is parallel to the magnetic field lines (θ = 0° or 180°), as sin(0°) = sin(180°) = 0.
Determining Direction: Fleming's Left-Hand Rule
While the formula gives us the magnitude of the force, we need a way to find its direction. This is where Fleming's Left-Hand Rule comes in handy! It's a visual mnemonic to help you remember the relative orientations of the force, magnetic field, and current.
Thumb: Represents the Force (F).
Forefinger: Represents the Magnetic Field (B), pointing from North to South.
Middle Finger: Represents the Conventional Current (I), from positive to negative.
Usage: Extend your thumb, forefinger, and middle finger of your left hand so they are all mutually perpendicular.
Force on a Moving Charged Particle
It's not just current-carrying wires that experience a force. Each individual charged particle moving through a magnetic field also feels a force! This is the microscopic origin of the force on a wire, as current is simply a flow of charged particles.
F = BQvsinθ
F: Force on the particle (in Newtons, N).
B: Magnetic flux density (in Tesla, T).
Q: Charge of the particle (in Coulombs, C).
v: Velocity of the particle (in meters per second, m/s).
θ: Angle between the particle's velocity and the magnetic field lines.
Direction: Use Fleming's Left-Hand Rule; the particle's velocity (v) replaces the current (I) for positive charges. For negative charges, reverse the direction of the middle finger or the final force direction.
Circular Motion of Charges in a Magnetic Field
A fascinating consequence of the force on a moving charge is what happens when the particle's velocity is perfectly perpendicular to the magnetic field. The magnetic force (F = BQv) is always directed at right angles to the velocity. In mechanics, a force that is always perpendicular to the velocity of an object causes it to move in a circle. Therefore, the magnetic force acts as a centripetal force.
The magnetic force provides the centripetal force: F_magnetic = F_centripetal.
Equating the formulas: BQv = mv²/r, where 'm' is the mass of the particle and 'r' is the radius of its circular path.
This relationship can be rearranged to find the radius of the circular path: r = mv / BQ.
This principle is crucial for applications like mass spectrometers, which separate particles based on their mass-to-charge ratio (m/Q), and particle accelerators like cyclotrons.
The Velocity Selector
Imagine needing to select particles that are all moving at a very specific speed. A velocity selector is a clever device that does exactly this! It uses a combination of perpendicular electric and magnetic fields to filter out particles based on their velocity.
Setup: Charged particles enter a region with a uniform electric field (E) and a uniform magnetic field (B) that are perpendicular to each other, and perpendicular to the initial velocity of the particles.
Balancing Forces: For a particle to pass through undeflected, the magnetic force (F_B = BQv) must perfectly balance the electric force (F_E = EQ).
Selection Condition: Setting F_B = F_E, we get BQv = EQ, which simplifies to the selected velocity: v = E/B.
Application: Useful in mass spectrometers and particle accelerators to prepare beams of particles with specific kinetic energies.
Worked examples
See the formulas applied — reveal one step at a time, like the exam.
A straight wire of length 0.25 m carrying a current of 3.0 A is placed in a uniform magnetic field of flux density 0.50 T. The wire is oriented at an angle of 60° to the magnetic field lines. Calculate the force acting on the wire.
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Identify the given values: B = 0.50 T, I = 3.0 A, L = 0.25 m, θ = 60°.
An electron is accelerated to a speed of 3.0 x 10^6 m/s and enters a region of uniform magnetic field of flux density 5.0 mT. The electron's velocity is perpendicular to the magnetic field. Calculate the magnitude of the force on the electron. (Charge of an electron, e = 1.60 x 10^-19 C)
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Identify the given values: B = 5.0 mT = 5.0 x 10^-3 T, Q = e = 1.60 x 10^-19 C, v = 3.0 x 10^6 m/s, θ = 90°.
How it all connects
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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.
- Fleming's Left-Hand Rule
This is where Fleming's Left-Hand Rule comes in handy! It's a visual mnemonic to help you remember the relative orientations of the force, magnetic field, and current.
- velocity selector
A velocity selector is a clever device that does exactly this!
- SI unit for magnetic
Tesla (T)
- Magnetic flux density (B)
Force per unit current per unit length on a straight wire placed perpendicular to the magnetic field.
- Motor effect
The phenomenon where a current-carrying conductor experiences a force when placed in an external magnetic field.
- purpose of a velocity
To allow only charged particles with a specific velocity to pass through undeflected, by balancing electric and magnetic forces.
- path of a charged
A circular path. The magnetic force provides the necessary centripetal force.
Quick check
Write your answer first, then compare it with the model one — the gap is what you would have lost.
Teach it back
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Revision flashcards
Guess first, then flip — retrieval beats re-reading.
Key takeaways
Review these before you close the topic — retrieval beats re-reading.
20.2 Force on a current-carrying conductor.
A current carrying conductor produces its own magnetic field.
When interacting with an external magnetic field, it will experience a force.
A current-carrying conductor will only experience a force if the current through it is perpendicular to the direction of the magnetic field lines.
Magnetic field strength is measured in magnetic flux density (B).
The units for B are in Tesla .
Practice — then mark it
The whole point: a real Cambridge question, marked mark-by-mark.
Determine the flux density B of the uniform magnetic field. Give a unit with your answer.
State how the magnetic force exerted on wire Y compares with the magnetic force exerted on wire X.
Extra simulations & links
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Frequently asked
Checkpoint
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Before you move on: do 9702/41 · Q5(c)(iii) on paper, snap a photo, and get examiner-style feedback on exactly where you win and lose marks.
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