In simple terms
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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.
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20.2 Force on a current-carrying conductor.
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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
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Key formulas
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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
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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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Glossary
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Quick check
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Revision flashcards
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What is the SI unit for magnetic flux density?
Tesla (T)
Key takeaways
Review these before you close the topic — retrieval beats re-reading.
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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.
9702/41 · Q5(c)(iii)
Determine the flux density B of the uniform magnetic field. Give a unit with your answer.
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