How a Loudspeaker Turns Current into Sound: The Motor Effect

Discover how a changing electrical current produces a force on a loudspeaker's voice coil, moving the cone to create sound waves. Follow the energy conversion, work through force calculations, and learn how the motor effect differs from electromagnetic induction.

November 5, 2026 17 min read

A loudspeaker can reproduce a 440 Hz tone by moving its cone in and out 440 times each second, yet nothing inside needs to rotate. An electrical signal somehow creates a force that moves the cone and pushes air towards your ears.

Predict this: when the current through the speaker coil reverses, must the magnetic field also reverse for the force to change direction?

No. The magnetic field can remain constant. Reversing the current reverses the force on the coil. This is the motor effect, and it is the key to understanding how a loudspeaker turns an electrical signal into sound.

01The components and the chain of cause and effect

A loudspeaker uses several components to turn a changing electrical current into mechanical motion.

Component	What it does
Amplifier	Supplies the electrical signal and the power needed to drive the speaker.
Permanent magnet	Produces a magnetic field in the region occupied by the voice coil.
Voice coil	A coil of wire that carries the changing current and experiences a magnetic force.
Cone or diaphragm	Moves with the coil and transfers energy to the surrounding air.
Surround and suspension	Keep the moving assembly aligned and provide a restoring force.
Air	Carries the resulting sound wave away from the speaker.

The voice coil is attached to the cone, so a force on the coil drives the cone as well. The magnet and coil are arranged so that the magnetic force moves the assembly along the cone’s axis.

For now, use a simplified model: the magnetic field is approximately constant, and the current through the coil follows the audio signal. Real speakers have electrical and mechanical complications, which we will return to later.

01The motor effect: how current produces force

Imagine a straight wire carrying current. Place it in an external magnetic field, and the wire experiences a force. This is the motor effect.

The force arises from the interaction between the magnetic field and the moving charges in the current-carrying conductor. The important point is that the conductor can experience a force even though the external magnetic field itself remains unchanged.

For a straight conductor perpendicular to a magnetic field,

\[ F = BIL \]

where:

\(F\) is the magnetic force, measured in newtons (N).
\(B\) is the magnetic flux density, measured in tesla (T).
\(I\) is the conventional current, measured in amperes (A).
\(L\) is the length of conductor within the magnetic field, measured in metres (m).

If the conductor is at an angle \(\theta\) to the magnetic field, the more general equation is

\[ F = BIL\sin\theta \]

The force is greatest when the conductor is perpendicular to the field and zero when it is parallel to the field.

What changes when the current reverses?

The direction of the force depends on both the current direction and the magnetic field direction. You can determine it using Fleming’s left-hand rule:

First finger: magnetic field direction, from north to south.
Second finger: conventional current direction.
Thumb: force direction.

Keep the magnetic field fixed and reverse the current. The force reverses.

If the current magnitude doubles while everything else stays constant, the force magnitude doubles too.

In a loudspeaker, the voice coil has many turns of wire. If each turn has an active wire length \(\ell\) in the field, and the forces on those sections add in the same direction, an idealised force estimate is

\[ F \approx BIn\ell \]

Here, \(n\) is the number of turns and \(\ell\) is the active length of wire per turn. This model assumes the active wire sections are perpendicular to the field and experience approximately the same field strength.

For a fixed magnetic field and speaker geometry, the force follows the current: when the current is positive, the force points in the chosen positive direction; when the current is negative, the force points in the opposite direction.

This is how an alternating electrical signal can produce an alternating magnetic force.

Worked example: calculating the force on a voice coil

A loudspeaker has a magnetic flux density of \(0.75\text{ T}\). Its voice coil has 24 turns, with \(0.018\text{ m}\) of active wire per turn. A current of \(0.40\text{ A}\) flows through the coil.

Assume the active wire sections are perpendicular to the magnetic field and their forces add in the same direction. Calculate the magnitude of the force on the coil.

Step 1

For the voice coil,

\[ F \approx BIn\ell \]

Step 2

\[ F \approx (0.75)(0.40)(24)(0.018) \]

Step 3

\[ F \approx 0.1296\text{ N} \]

To two significant figures,

\[ \boxed{F \approx 0.13\text{ N}} \]

Step 4

The coil experiences a force of approximately \(0.13\text{ N}\). The force’s direction depends on the directions of the current and magnetic field, which can be determined using Fleming’s left-hand rule.

If the current reverses to \(-0.40\text{ A}\), the force has the same magnitude but the opposite direction.

02Why the cone follows the signal, but not instantly

The voice coil is attached to the cone. When the coil experiences a force, the cone is driven along with it.

As the audio current changes, the motor-effect force changes. An alternating current therefore drives the coil and cone back and forth.

But there is an important distinction between the direction of a force and the direction of motion.

Imagine pushing a shopping trolley forwards and then applying a backwards force. The trolley does not instantly travel backwards. The force first changes its acceleration, slowing its forward motion before it can reverse direction.

The analogy is not a complete model of a loudspeaker, which also has a flexible suspension and an electrically driven coil. However, the distinction between force and motion is exactly the same.

Newton’s second law states that

\[ F_{\text{net}} = ma \]

where \(F_{\text{net}}\) is the net force, \(m\) is the moving mass, and \(a\) is the acceleration.

A change in net force changes the acceleration. It does not instantly reverse the velocity.

This matters when interpreting a speaker’s motion. If the current reverses while the cone is still moving outwards, the magnetic force can point inwards while the cone continues moving outwards for a short time. The cone slows, reaches a turning point, and then moves inwards.

The suspension also exerts a restoring force, while damping removes some of the moving assembly’s energy. These effects influence how the cone responds to the electrical signal.

Consequently, the current waveform and the cone’s displacement are not necessarily in phase. The force may follow the current closely in our simplified model, but the cone’s position depends on its inertia, suspension, and damping as well.

Worked example: a changing current and force

An amplifier supplies a sinusoidal current to a loudspeaker:

\[ I(t)=0.30\sin(2\pi ft)\text{ A} \]

The frequency is \(250\text{ Hz}\). The voice coil has 40 turns, an active wire length of \(0.020\text{ m}\) per turn, and sits in a magnetic field of \(0.60\text{ T}\).

Take the outward direction as positive.

Calculate:

The period of the current.
The maximum motor-effect force.
The force at \(t=3.0\text{ ms}\).

Step 1

The period \(T\) is the time for one complete cycle:

\[ T=\frac{1}{f} =\frac{1}{250} =0.0040\text{ s} \]

Therefore,

\[ T=4.0\text{ ms} \]

Step 2

The current reaches a maximum magnitude of \(0.30\text{ A}\). Using the voice-coil force equation,

\[ F_{\max}=Bn\ell I_{\max} \]

\[ F_{\max}=(0.60)(40)(0.020)(0.30) \]

\[ F_{\max}=0.144\text{ N} \]

The maximum force magnitude is \(0.144\text{ N}\).

Step 3

Convert the time to seconds:

\[ t=0.0030\text{ s} \]

Substitute into the current equation:

\[ I(0.0030) =0.30\sin(2\pi\times250\times0.0030) \]

\[ I(0.0030) =0.30\sin\left(\frac{3\pi}{2}\right) =-0.30\text{ A} \]

The current is negative, so the motor-effect force points inwards.

Step 4

\[ F=(0.60)(40)(0.020)(-0.30) \]

\[ F=-0.144\text{ N} \]

The force is \(0.144\text{ N}\) inwards.

Notice what this result does not tell you: it does not prove that the cone is moving inwards at that instant. It tells you the direction of the magnetic force. The cone’s velocity depends on its motion immediately beforehand and on the other forces acting on it.

03How cone motion becomes sound

The cone is not just moving for the sake of it. Its job is to transfer energy to the surrounding air.

When the cone moves outwards, it pushes on the nearby air. This creates a region of higher pressure called a compression.

When the cone moves inwards, it moves away from the air in front of it, creating a region of lower pressure called a rarefaction.

As the cone oscillates, it produces a changing pattern of compressions and rarefactions. These pressure disturbances travel through the air as a sound wave.

Sound in air is a longitudinal wave. The air particles oscillate back and forth approximately parallel to the direction in which the wave travels.

The particles do not travel all the way from the speaker to your ear. Instead, the disturbance transfers energy through successive regions of air.

The electrical signal therefore controls the pattern of motion that produces the sound:

The signal’s frequency determines the frequency of the driving current and, when reproduced faithfully, the sound’s frequency. This is closely related to pitch.
The signal’s amplitude affects the current and motor-force amplitude. This generally affects the sound’s pressure amplitude and perceived loudness.
The speaker’s mechanical and acoustic properties affect how faithfully it converts the driving force into sound at different frequencies.

A larger current does not automatically produce a proportionally louder sound in every situation. The cone, suspension, enclosure, and speaker’s frequency response all matter.

Following the energy

The motor effect explains the force, but the energy transfer is just as important.

The amplifier supplies electrical energy. The motor effect produces a force on the coil, causing the moving assembly to do mechanical work. The cone transfers some of that energy to the air as sound.

Not all the electrical energy becomes sound. Some is dissipated as heat in the voice coil because of its electrical resistance, while mechanical losses also remove energy from the moving assembly.

04Motor effect versus electromagnetic induction

These two ideas are closely related, and a loudspeaker can involve both. However, they describe different physical processes.

Feature	Motor effect	Electromagnetic induction
What causes it?	Current-carrying conductor in a magnetic field	Changing magnetic flux linkage through a circuit
Immediate result	A force acts on the conductor	An induced electromotive force (emf) is produced
What happens next?	The conductor can accelerate and move	Current flows if the circuit provides a closed path
Role in a loudspeaker	Drives the voice coil and cone	The moving coil can generate a back emf

The distinction comes down to cause and effect.

In normal operation, the amplifier supplies current to the voice coil. That current interacts with the permanent magnet’s field, producing the motor-effect force that drives the cone.

As the coil moves, its motion through the magnetic field changes its magnetic flux linkage. This produces an induced emf. In a loudspeaker, this is commonly called the back emf.

The induced emf affects the electrical behaviour of the coil. Its direction follows Lenz’s law: it opposes the change in magnetic flux that produces it. It can therefore oppose the applied electrical drive and influence the current drawn from the amplifier.

Both processes can occur at once, but they answer different questions:

The motor effect explains how the current produces a force that drives the coil.
Electromagnetic induction explains how the coil’s motion can produce a voltage.

A common mistake is to say that electromagnetic induction is what initially pushes the cone. In the normal operating model, the amplifier supplies the driving current, and the motor effect produces the driving force. Induction is an additional effect arising from the coil’s motion.

06Questions and solutions

Question 1

A loudspeaker’s voice coil has 25 turns, with \(0.016\text{ m}\) of active wire per turn in a magnetic field of \(0.40\text{ T}\). A current of \(0.30\text{ A}\) flows through the coil.

Assume the active wire sections are perpendicular to the magnetic field and the forces add in the same direction.

Calculate the magnitude of the force on the voice coil.

Solution 1

The force on the voice coil is \(0.048\text{ N}\). Each turn experiences a motor-effect force, and the forces on the active wire sections add together.

For a coil with \(n\) turns,

\[ F\approx BIn\ell \]

Substitute the values:

\[ F\approx(0.40)(0.30)(25)(0.016) \]

\[ F\approx0.048\text{ N} \]

The coil experiences a force of \(4.8\times10^{-2}\text{ N}\). The direction depends on the current and magnetic field directions, which can be determined using Fleming’s left-hand rule.

Question 2

Two hypothetical coils carry a current of \(0.40\text{ A}\) in a magnetic field of \(0.50\text{ T}\).

Coil A has 24 turns, with \(0.020\text{ m}\) of active wire per turn. The wire is perpendicular to the field.
Coil B has 30 turns, with \(0.015\text{ m}\) of active wire per turn. The wire is at an angle of \(60^\circ\) to the field.

Assume the forces on the active wire sections add in the same direction.

Which coil experiences the greater force? Calculate both forces and explain why the number of turns alone is not enough to decide.

Solution 2

Coil A experiences the greater force: \(0.096\text{ N}\), compared with approximately \(0.078\text{ N}\) for coil B. Although coil B has more turns, its active wire length per turn is shorter, and its wire is less favourably oriented relative to the field.

For coil A, use the general motor-effect equation:

\[ F_A=BI n_A\ell_A\sin90^\circ \]

\[ F_A=(0.50)(0.40)(24)(0.020) \]

\[ F_A=0.096\text{ N} \]

For coil B,

\[ F_B=BI n_B\ell_B\sin60^\circ \]

\[ F_B=(0.50)(0.40)(30)(0.015)(0.866) \]

\[ F_B\approx0.078\text{ N} \]

The tempting prediction is that coil B must experience the greater force because it has more turns. That ignores two other factors: the active wire length and the angle between the wire and the magnetic field.

The force depends on the combined effect of the field strength, current, number of turns, active wire length, and orientation. Comparing just one factor can give the wrong answer.

Question 3

During normal operation, an amplifier drives current through a loudspeaker’s voice coil. The coil moves in the permanent magnet’s field, and an induced voltage appears across the coil.

A student concludes:

“The coil must be moving because electromagnetic induction creates the voltage that pushes it.”

Explain why this reasoning is incorrect. Identify the role of the motor effect and the role of electromagnetic induction, and explain how both can occur during the same operation.

Solution 3

The motor effect is the main driving mechanism, while electromagnetic induction produces the back emf as the coil moves. The induced voltage is evidence of the coil’s motion, not the original explanation for the force that drives it.

The amplifier supplies current to the voice coil. The current-carrying coil experiences a force in the permanent magnet’s field, producing motion through the motor effect.

As the coil moves, its magnetic flux linkage changes, inducing an emf. This back emf influences the electrical circuit and can affect the current supplied by the amplifier.

The two processes therefore occur in a linked sequence:

The amplifier supplies current to the coil.
The motor effect produces a force on the coil.
The coil and cone move.
The moving coil produces an induced emf through electromagnetic induction.
The induced emf affects the electrical behaviour of the speaker.

The student’s mistake is to confuse a consequence of the coil’s motion with the original driving mechanism. Induction and the motor effect are related, but they are not interchangeable terms.

Question 4

At an instant \(t=0\), a speaker cone passes through its equilibrium position while moving outwards.

Assume that positive current produces an outward motor-effect force. At \(t=0\), the current switches instantly from \(+I_0\) to \(-I_0\) and remains negative for the next few milliseconds. The suspension’s restoring force is zero at equilibrium, and damping can be ignored.

Explain:

(a) The direction of the motor-effect force immediately after the current switches.

(b) The direction in which the cone is moving immediately after the switch.

(d) Whether a pressure disturbance already travelling away from the speaker reverses direction when the current switches.

Solution 4

The motor-effect force reverses and points inwards, but the cone initially continues moving outwards. It slows, reaches a turning point, and then moves inwards. A pressure disturbance already travelling away from the speaker continues propagating away.

(a) Motor-effect force

Reversing the current reverses the force because the magnetic field remains unchanged. The current is now negative, so the force points inwards.

(b) Immediate direction of motion

The cone is still moving outwards immediately after the switch. Its velocity cannot reverse instantaneously under an ordinary finite force.

At the instant it passes through equilibrium, the suspension’s restoring force is zero. The inward motor-effect force therefore produces an inward net force and an inward acceleration.

(c) Motion before the first inward movement

The inward acceleration first slows the cone’s outward motion. As the cone moves farther out, the suspension also exerts an inward restoring force.

The cone eventually reaches a turning point, where its outward velocity becomes zero. It then begins moving inwards.

The key distinction is that the force determines the acceleration, while the cone’s existing velocity determines its immediate direction of motion.

(d) The pressure disturbance

The sound disturbance already travelling through the air continues to propagate away from the speaker. Reversing the electrical current does not reverse a wave that is already travelling through the air.

The cone’s later motion creates further pressure changes, but those changes do not make the earlier disturbance travel backwards.

Question 5

Two identical loudspeakers have their cones pushed outwards and released with the same initial velocity. Their amplifiers are disconnected, and the cones and suspensions have identical mechanical losses.

In speaker A, the voice-coil circuit is left open.
In speaker B, the voice coil is connected through a low-resistance external resistor.

Assume both coils move through the same magnetic field. The moving coil produces an induced emf proportional to its speed, and the circuit in speaker B is closed so that the induced current can flow.

A student argues that speaker B should keep moving for longer because its induced current provides an extra motor-effect force to keep the cone moving.

Determine which speaker’s motion dies away faster. Explain the complete chain from motion to induction, current, force, energy transfer, and sound. Then explain what would happen if the resistance in speaker B were increased towards an open circuit.

Solution 5

Speaker B’s motion dies away faster because its induced current produces a motor-effect force that opposes the coil’s motion. The induced current does not provide an extra driving force; it produces electromagnetic damping that transfers mechanical energy into electrical energy and then heat.

Step 1: The moving coil produces an induced emf.

Both coils are initially moving through the magnetic field. Their motion changes the magnetic flux linkage, producing an induced emf.

The magnitude of this emf depends on the coil’s speed in the simplified model. At the initial instant, the two coils have the same speed, so their induced emfs have the same magnitude.

Step 2: The circuit determines whether current flows.

In speaker A, the circuit is open. An induced emf can exist, but there is no sustained current through the open circuit.

In speaker B, the circuit is closed through a resistor. The induced emf drives a current through the coil and resistor.

If the coil has resistance \(r\) and the external resistor has resistance \(R\), the current magnitude is

\[ I_{\text{ind}}=\frac{\mathcal{E}}{R+r} \]

where \(\mathcal{E}\) is the induced emf.

A low external resistance allows a larger induced current than a high external resistance, for the same induced emf.

Step 3: The induced current produces a force.

The current in speaker B’s voice coil interacts with the permanent magnet’s field. This produces a motor-effect force.

Lenz’s law determines the direction of the induced current so that the resulting electromagnetic effect opposes the change that produced it. In this situation, the induced current produces a force that opposes the coil’s motion.

This is the crucial interaction: induction produces the emf, the closed circuit allows current to flow, and the motor effect converts that current into a force opposing the motion.

The student has mistaken an opposing force for an extra driving force.

Step 4: Mechanical energy is transferred and dissipated.

In speaker B, the opposing force removes kinetic energy from the moving cone and coil. The induced current transfers this energy into the electrical circuit, where it is dissipated as heat in the coil and resistor.

Speaker A has no comparable electromagnetic braking force because its open circuit prevents appreciable induced current from flowing. Its motion still loses energy through the ordinary mechanical losses of the cone and suspension, but it lacks the additional electromagnetic damping.

Therefore, speaker B’s oscillation dies away faster, and its sound rings for a shorter time after the initial push.

Step 5: Increase the resistance.

As the external resistance \(R\) increases, the induced current decreases for the same induced emf. The opposing motor-effect force becomes smaller, so the electromagnetic damping decreases.

As the resistance becomes very large, the circuit approaches the open-circuit condition. The induced emf may still exist, but the current and the resulting electromagnetic braking force approach zero.

The important distinction is that an induced emf does not automatically mean a large induced current or a large force. The circuit conditions determine the current, and the current determines the motor-effect force.

This example brings the two magnetic effects together. To predict how a real loudspeaker responds to different audio frequencies, the next step is to combine the motor-effect force with the cone’s mass, suspension, damping, and the back emf produced by its motion.