Magnetic Forces and Fields in Systems
4. Motors and loudspeakers
Learning outcomes
- I can explain how electric motors operate.
- I can describe the role of magnetic forces in motors.
- I can explain how loudspeakers convert electrical energy into sound.
- I can identify key components of motors and speakers.
- I can relate magnetic force principles to electromechanical devices.
Motors and Loudspeakers
Electricity, Magnetism, and Motion
Electric motors and loudspeakers are examples of electromechanical devices. They use interactions between electric currents and magnetic fields to produce mechanical motion.
The key principle is the motor effect:
A current-carrying conductor placed in a magnetic field can experience a force.
For a straight conductor:
F = BIL sin θ
where:
- F = magnetic force (N)
- B = magnetic flux density (T)
- I = current (A)
- L = length of conductor in the magnetic field (m)
- θ = angle between the current and magnetic field
When the conductor is perpendicular to the field:
F = BIL
This simple principle allows electrical energy to produce movement.
The Motor Effect
Electric current consists of moving charges.
When these moving charges pass through a magnetic field, they experience magnetic forces.
In a wire, these forces are transferred to the conductor.
Therefore:
electric current + magnetic field → force on conductor
The direction of this force can be determined using Fleming's Left-Hand Rule.
Fleming's Left-Hand Rule
Hold the thumb, first finger, and second finger of your left hand mutually perpendicular.
First finger
Represents the magnetic:
Field
Second finger
Represents conventional:
Current
Thumb
Represents:
Force or Motion
A useful memory aid is:
First = Field
seCond = Current
thuMb = Motion
What Is an Electric Motor?
An electric motor is a device that converts:
electrical energy → mechanical energy
Motors are found in:
- electric vehicles
- fans
- pumps
- washing machines
- refrigerators
- elevators
- drones
- power tools
- computer cooling systems
- industrial machinery
- robots
Although motors can have very different designs, their operation ultimately involves magnetic forces.
The Simple DC Motor
A simple DC motor provides a useful model for understanding how electric motors work.
Important components include:
- permanent magnets or electromagnets
- rotating coil
- axle
- split-ring commutator
- brushes
- DC power supply
Magnetic Field
A simple motor contains a magnetic field produced by:
- permanent magnets
or:
- electromagnets
The coil is positioned within this field.
A strong magnetic field helps produce a large force because:
F ∝ B
The Current-Carrying Coil
Electric current flows through a coil of wire located inside the magnetic field.
Opposite sides of the coil carry current in opposite directions.
Because force direction depends on current direction, the two sides experience forces in opposite directions.
One side may be pushed upward while the other is pushed downward.
These forces create a:
turning effect
Torque
The turning effect of a force is called:
torque
The forces on opposite sides of the coil form a couple.
Instead of simply pushing the entire coil in one direction, the forces cause it to rotate.
The motor effect therefore converts magnetic forces into rotational motion.
How the Coil Begins to Rotate
Suppose one side of the coil carries current into the page while the opposite side carries current out of the page.
Using Fleming's Left-Hand Rule:
- one side experiences an upward force
- the opposite side experiences a downward force
These forces create torque around the axle.
The coil begins to rotate.
The Problem After Half a Turn
If the current direction remained unchanged, the forces would eventually produce torque in the opposite rotational direction after the coil had turned through approximately half a rotation.
The coil would not continue rotating smoothly in the same direction.
A simple DC motor solves this problem using the:
split-ring commutator
Split-Ring Commutator
The split-ring commutator reverses the current through the rotating coil every half-turn.
The sequence is:
coil rotates
↓
half-turn completed
↓
commutator changes electrical contact
↓
current through coil reverses
↓
magnetic forces reverse
↓
torque continues rotation in the same overall direction
This allows continuous rotation.
Brushes
The brushes provide electrical contact between the stationary power supply and the rotating commutator.
Traditionally, brushes may be made from carbon-based materials.
Their purpose is to allow current to flow into and out of the rotating coil while the motor is operating.
In a simple model:
power supply → brushes → commutator → coil
Axle
The rotating coil is attached to an:
axle
The torque on the coil rotates the axle.
The axle can then transfer mechanical energy to another device.
For example, the axle might turn:
- a fan blade
- a wheel
- a pump
- a gear system
Energy Transfer in a Motor
A motor converts electrical energy into mechanical energy.
The useful energy pathway can be summarized as:
electrical energy → magnetic interaction → rotational kinetic energy
However, real motors are not 100% efficient.
Some energy is transferred to the surroundings through:
- heating in wires
- friction
- sound
- magnetic losses
Therefore:
electrical input energy = useful mechanical energy + energy dissipated
Increasing the Force in a Motor
For a conductor perpendicular to the field:
F = BIL
Therefore, the force can be increased by increasing:
Magnetic flux density
Larger B → larger force
Current
Larger I → larger force
Length of conductor in the magnetic field
Larger L → larger force
A motor can therefore be made more powerful by carefully controlling these factors.
Increasing Motor Torque
Motor torque can also be increased by:
- increasing the current
- increasing magnetic field strength
- increasing the number of turns in the coil
- increasing coil area
- optimizing the orientation of the coil and magnetic field
For an ideal current-carrying coil:
τ = NBIA sin θ
where:
- τ = torque (N·m)
- N = number of turns
- B = magnetic flux density (T)
- I = current (A)
- A = coil area (m²)
- θ = angle between the coil's magnetic moment and the field
Why More Turns Help
Suppose a coil contains many loops of wire.
Each loop experiences magnetic forces.
The turning effects from the loops combine.
Therefore:
more turns → greater torque
provided other conditions remain the same.
This is why practical motor windings contain many turns rather than a single loop.
Reversing Motor Direction
The direction of motor rotation can be reversed by reversing either:
- current direction
or:
- magnetic-field direction
If both are reversed simultaneously, the direction of force remains unchanged.
This follows directly from the motor effect.
Permanent-Magnet Motors
Some motors use permanent magnets to provide the magnetic field.
Modern high-strength permanent magnets can produce powerful magnetic fields in compact devices.
Permanent-magnet motors are common in:
- electric vehicles
- drones
- computer equipment
- robotics
- power tools
Electromagnetic Motors
Other motors use electromagnets to create some or all of their magnetic fields.
This allows engineers to control magnetic-field strength using electric current.
Modern motors may use sophisticated electronic control systems instead of the simple mechanical commutator found in introductory DC motor models.
The underlying principle remains:
magnetic fields interacting with electric currents produce forces and torque.
Motor Components
| Component | Function |
|---|---|
| Magnetic field source | Provides the magnetic field |
| Coil/winding | Carries current |
| Rotor | Rotating part of the motor |
| Stator | Stationary part of the motor |
| Axle/shaft | Transfers rotational motion |
| Commutator | Reverses current in a simple brushed DC motor |
| Brushes | Provide electrical contact with the rotating commutator |
| Power supply | Provides electrical energy |
Not every motor contains all these components. For example, many modern motors do not use brushes or a mechanical commutator.
Rotor and Stator
Two important motor terms are:
Rotor
The part that rotates.
Stator
The stationary part surrounding or interacting with the rotor.
Depending on the motor design, permanent magnets or electromagnets may be located on either the rotor or stator.
From Motors to Loudspeakers
A loudspeaker uses the same fundamental motor effect.
However, instead of producing continuous rotation, a loudspeaker produces:
back-and-forth motion
This movement creates sound waves.
Therefore, motors and loudspeakers are closely related electromechanical devices.
What Is a Loudspeaker?
A loudspeaker converts:
electrical energy → mechanical vibration → sound energy
Important components include:
- permanent magnet
- voice coil
- cone or diaphragm
- flexible suspension
- frame
- electrical connections
The Permanent Magnet
A loudspeaker usually contains a strong permanent magnet.
The magnet creates a magnetic field in the region surrounding the:
voice coil
The magnetic structure is designed so that a strong field passes through the coil.
The Voice Coil
The voice coil is a lightweight coil of wire connected to the speaker cone.
The audio signal passes through the coil as an electric current.
Because the coil is located in a magnetic field, it experiences a magnetic force.
The force is related to:
F = BIL
for sections of conductor appropriately oriented to the field.
Why the Voice Coil Moves
When current flows through the voice coil:
current + magnetic field → magnetic force
The force moves the coil.
Because the coil is attached to the cone:
coil moves → cone moves
When the current reverses:
force reverses
Therefore:
coil moves in the opposite direction
Alternating Audio Signals
An audio signal changes continuously.
The current through the voice coil therefore changes:
- magnitude
- direction
As the current changes direction, the magnetic force also changes direction.
Therefore, the voice coil moves:
back and forth
The cone follows this motion.
Producing Sound Waves
The moving speaker cone pushes and pulls on the surrounding air.
When the cone moves outward, it compresses nearby air.
When it moves inward, it produces a region of lower pressure.
This produces alternating:
- compressions
- rarefactions
These pressure disturbances travel through the air as:
sound waves
Therefore:
electrical signal → changing current → changing magnetic force → cone vibration → sound wave
Frequency and Pitch
If the current changes direction rapidly, the speaker cone vibrates rapidly.
The frequency of the cone's vibration determines the frequency of the sound wave.
Higher frequency generally produces:
higher pitch
Lower frequency generally produces:
lower pitch
For example:
200 Hz electrical signal
↓
speaker vibrates approximately 200 times per second
↓
sound wave frequency ≈ 200 Hz
Amplitude and Loudness
A larger current can produce a larger magnetic force.
From:
F ∝ I
a stronger current can produce greater cone displacement, within the operating limits of the speaker.
Greater vibration amplitude generally produces a sound wave with greater amplitude.
This is perceived as:
greater loudness
Therefore:
signal frequency → sound frequency/pitch
signal amplitude → vibration amplitude/loudness
Example: Speaker Force
Suppose the effective conductor length in a voice coil is:
L = 0.50 m
The current is:
I = 0.40 A
The magnetic flux density is:
B = 0.60 T
Assume the conductor is perpendicular to the field.
Use:
F = BIL
F = (0.60)(0.40)(0.50)
F = 0.12 N
If the current reverses, the force becomes:
0.12 N in the opposite direction
This reversal allows the cone to vibrate.
Why the Cone Is Lightweight
The speaker cone and voice coil should respond rapidly to changes in the electrical signal.
A lower mass allows them to accelerate more easily.
From:
F = ma
a given force produces greater acceleration when mass is smaller.
This helps the speaker reproduce rapidly changing sounds accurately.
Speaker Suspension
The speaker cone cannot move freely without control.
A flexible suspension:
- supports the cone
- allows back-and-forth movement
- helps return the cone toward equilibrium
- keeps the voice coil correctly positioned
The speaker therefore behaves partly like a mechanical oscillating system.
Motors vs Loudspeakers
Both devices use the same basic principle:
current + magnetic field → force
But they use the force differently.
| Electric Motor | Loudspeaker |
|---|---|
| Produces rotational motion | Produces back-and-forth motion |
| Converts electrical energy to mechanical rotation | Converts electrical energy to vibration and sound |
| Usually uses coils and magnetic fields | Uses a voice coil and permanent magnet |
| Torque rotates a rotor | Force vibrates a diaphragm |
| Used to drive machines | Used to produce sound |
Headphones and Earbuds
Many headphones use the same basic principle as loudspeakers.
An electrical audio signal passes through a small coil.
The coil interacts with a magnetic field.
The resulting force moves a small diaphragm.
The diaphragm produces sound waves.
Because headphones operate close to the ear, the required diaphragm motion can be much smaller than in a large loudspeaker.
Microphones: The Reverse Idea
Some microphones use electromagnetic principles in approximately the reverse direction.
In a dynamic microphone:
sound waves
↓
diaphragm vibrates
↓
coil moves in magnetic field
↓
voltage is induced
↓
electrical audio signal
A loudspeaker converts electrical signals into sound.
A dynamic microphone converts sound into electrical signals.
This illustrates the close relationship between electricity, magnetism and mechanical motion.
Other Electromechanical Devices
The motor effect is used in many technologies.
Examples include:
- electric motors
- loudspeakers
- headphones
- moving-coil meters
- actuators
- some vibration systems
- robotic mechanisms
- electromagnetic control systems
These devices convert electrical signals into mechanical movement.
Moving-Coil Meters
A moving-coil meter contains a coil in a magnetic field.
When current flows, the coil experiences torque.
A larger current produces a larger torque.
The coil rotates against a restoring mechanism and moves a pointer.
The amount of deflection can therefore indicate the current.
This principle has been used in analogue:
- ammeters
- voltmeters
- galvanometers
Practical Example: Electric Vehicle Motor
An electric vehicle uses electrical energy stored in its battery.
The motor converts this energy into rotational mechanical energy.
A simplified energy pathway is:
battery
↓
electrical current
↓
controlled magnetic fields
↓
magnetic forces and torque
↓
rotating motor shaft
↓
wheels
Modern electric-vehicle motors are far more sophisticated than the simple classroom DC motor, but magnetic force remains central to their operation.
Practical Example: Cooling Fan
A computer cooling fan contains a small electric motor.
Electrical energy produces magnetic interactions within the motor.
These produce torque.
The rotor turns.
The attached fan blades move air through the computer.
Therefore:
electrical energy → rotational kinetic energy → moving air
Practical Example: Loudspeaker
For a loudspeaker:
audio electrical signal
↓
changing current in voice coil
↓
changing magnetic force
↓
voice coil moves
↓
cone vibrates
↓
air vibrates
↓
sound reaches listener
The speaker therefore reproduces information contained in the electrical signal as variations in air pressure.
Magnetic Force as an Energy-Conversion Mechanism
Magnetic force provides an important connection between electrical and mechanical systems.
A current can produce:
- linear motion
- rotation
- vibration
depending on how the conductor and magnetic field are arranged.
This allows engineers to design many different electromechanical devices using the same fundamental physics.
Common Mistakes
Mistake: Saying a motor works because magnets simply attract the coil.
The key effect is the force on a current-carrying conductor in a magnetic field.
Mistake: Saying both sides of a motor coil experience forces in the same direction.
Opposite current directions produce opposite forces, creating torque.
Mistake: Confusing force with torque.
Force acts on the conductors; the arrangement of forces produces torque.
Mistake: Saying the split-ring commutator increases the current.
Its main role in a simple DC motor is to reverse current every half-turn.
Mistake: Saying the brushes produce the magnetic field.
Brushes provide electrical contact with the rotating commutator.
Mistake: Saying a loudspeaker's permanent magnet moves back and forth.
In a typical speaker, the voice coil and attached cone move.
Mistake: Saying sound comes directly from the electric current.
The current produces magnetic force, which moves the cone, which then produces sound waves in the air.
Mistake: Saying frequency mainly determines loudness.
Frequency is closely associated with pitch; amplitude is associated with loudness.
Mistake: Saying a loudspeaker and motor use unrelated physics.
Both rely fundamentally on magnetic forces acting on current-carrying conductors.
Key Terms
Electric motor — device that converts electrical energy into mechanical energy.
Motor effect — force experienced by a current-carrying conductor in a magnetic field.
Magnetic force — force produced by the interaction between a current and magnetic field.
Torque — turning effect of a force.
Couple — pair of forces that produces a turning effect.
Rotor — rotating part of a motor.
Stator — stationary part of a motor.
Coil — loops of conducting wire carrying electric current.
Split-ring commutator — component that reverses current through the coil of a simple DC motor every half-turn.
Brushes — stationary electrical contacts that supply current to the rotating commutator.
Axle — shaft that carries rotational motion from a motor.
Loudspeaker — device that converts an electrical audio signal into sound.
Voice coil — current-carrying coil in a loudspeaker that moves within a magnetic field.
Diaphragm — flexible vibrating surface that produces sound waves.
Electromechanical device — device that converts between electrical and mechanical forms of energy or signals.
Key Takeaways
- Motors and loudspeakers rely on the motor effect.
- A current-carrying conductor experiences a force in a magnetic field.
- For a straight conductor, F = BIL sin θ.
- Fleming's Left-Hand Rule determines the force direction.
- A motor converts electrical energy into mechanical energy.
- Opposite sides of a current-carrying motor coil experience forces in opposite directions.
- These forces create torque.
- The rotor is the rotating part of a motor.
- The stator is the stationary part.
- In a simple DC motor, the split-ring commutator reverses current every half-turn.
- The brushes maintain electrical contact with the rotating commutator.
- Increasing current or magnetic flux density can increase magnetic force.
- Increasing the number of coil turns can increase motor torque.
- A loudspeaker converts an electrical audio signal into mechanical vibration and then sound.
- Current through the voice coil interacts with a permanent magnetic field.
- Reversing the current reverses the force on the voice coil.
- The voice coil therefore moves back and forth.
- The attached cone or diaphragm produces pressure variations in the air.
- Signal frequency determines the frequency of the produced sound.
- Motors, speakers, headphones and many actuators apply the same fundamental magnetic-force principles.
Check Your Understanding
- What is the motor effect?
- State the equation for the force on a current-carrying conductor in a magnetic field.
- Explain why opposite sides of a motor coil experience forces in opposite directions.
- What is torque?
- Describe how magnetic forces produce rotation in a simple DC motor.
- What is the purpose of the split-ring commutator?
- Why must the current in a simple DC motor reverse every half-turn?
- What is the function of the brushes?
- Distinguish between the rotor and stator.
- State three ways of increasing the turning effect of a motor.
- Explain how reversing the current affects motor rotation.
- Describe the energy conversion occurring in an electric motor.
- Identify the major components of a simple loudspeaker.
- What is the function of the voice coil?
- Explain why the voice coil moves when current passes through it.
- Why does an alternating audio signal cause the speaker cone to vibrate?
- Explain how cone vibration produces sound waves.
- How does the frequency of the electrical signal affect the sound produced?
- A speaker voice coil has an effective conductor length of 0.80 m in a 0.50 T magnetic field and carries 0.30 A. Assuming perpendicular orientation, calculate the magnetic force.
- Compare an electric motor and a loudspeaker, explaining how both use the same magnetic-force principle to produce different forms of mechanical motion.