Applications of Electromagnetic Induction
4. Wireless Power Transfer
Learning outcomes
- I can explain how wireless charging uses electromagnetic induction.
- I can describe how energy is transferred between coils.
- I can identify factors affecting charging efficiency.
- I can explain practical applications of wireless power systems.
- I can discuss advantages and limitations of wireless charging.
Wireless Power Transfer
Wireless power transfer is the transfer of electrical energy from a power source to a device without a direct electrical connection between them.
A common form of wireless charging uses electromagnetic induction. Alternating current in a transmitter coil produces a changing magnetic field. This changing magnetic field passes through a nearby receiver coil and induces an EMF.
The basic process is:
electrical energy → alternating current → changing magnetic field → induced EMF → electrical current → stored or useful electrical energy
Wireless charging is commonly used for smartphones, watches, earbuds, electric toothbrushes, medical devices, and increasingly for larger systems such as electric vehicles.
Electromagnetic Induction
Wireless charging relies on Faraday's law of electromagnetic induction.
A changing magnetic flux through a coil produces an induced EMF:
ε = −N ΔΦ/Δt
where:
- ε = induced EMF
- N = number of turns in the coil
- ΔΦ = change in magnetic flux
- Δt = time interval
The important requirement is changing magnetic flux.
A steady magnetic field does not continuously induce an EMF in a stationary receiver coil.
The Transmitter Coil
A wireless charger contains a transmitter coil, sometimes called the primary coil.
Electronic circuitry supplies alternating current to this coil.
The alternating current produces a changing magnetic field:
AC → changing magnetic field
Because the current repeatedly changes direction, the magnetic field also changes.
This changing field extends into the region around the transmitter.
The Receiver Coil
The device being charged contains a receiver coil, sometimes called the secondary coil.
When the receiver is placed close to the transmitter:
- changing magnetic flux passes through the receiver coil
- an EMF is induced
- electrical current can flow
- electronic circuits process the electrical energy
- the energy can be supplied to the device or battery
The two coils therefore transfer energy electromagnetically rather than through exposed electrical contacts.
Similarity to a Transformer
Wireless inductive charging is closely related to transformer operation.
A transformer uses:
primary coil → changing magnetic flux → secondary coil
Wireless charging uses the same basic principle.
However, in a conventional transformer:
- the coils are usually closely coupled
- they often share a magnetic core
- very little distance separates them
In wireless charging:
- the coils are physically separated
- there is usually an air gap
- not all magnetic flux from the transmitter links the receiver
Wireless charging can therefore be thought of as a form of loosely coupled transformer action.
Energy Transfer Between the Coils
The complete process can be followed step by step.
Step 1:
Electrical energy is supplied to the transmitter.
Step 2:
Electronic circuitry produces alternating current in the transmitter coil.
Step 3:
The alternating current creates a changing magnetic field.
Step 4:
The changing magnetic field passes through the receiver coil.
Step 5:
Changing magnetic flux induces an EMF in the receiver coil.
Step 6:
The induced EMF produces electrical current.
Step 7:
Electronic circuitry converts and regulates the received electrical energy.
Step 8:
The energy powers the device or charges its battery.
Magnetic Flux
Magnetic flux through a coil can be represented by:
Φ = BA cos θ
where:
- Φ = magnetic flux
- B = magnetic field strength
- A = area of the coil
- θ = angle between the magnetic field and the normal to the coil
This equation helps explain why the orientation of wireless charging coils matters.
Maximum flux occurs when the magnetic field passes through the coil in the most favorable orientation.
Coil Alignment
For efficient wireless charging, the transmitter and receiver coils should usually be reasonably well aligned.
Good alignment allows more of the transmitter's magnetic field to pass through the receiver coil.
Poor alignment can result in:
- reduced magnetic flux linkage
- lower induced EMF
- slower charging
- greater energy losses
- additional heating
This is why many wireless charging devices indicate where the device should be positioned.
Distance Between the Coils
Distance also strongly affects wireless power transfer.
As the receiver moves farther from the transmitter:
- magnetic coupling generally becomes weaker
- less magnetic flux links the receiver coil
- induced EMF decreases
- charging efficiency can decrease
This is why ordinary inductive chargers generally operate over relatively short distances.
Magnetic Coupling
Magnetic coupling describes how effectively the magnetic field produced by one coil links with another coil.
Strong coupling means a larger fraction of the transmitter's magnetic field interacts effectively with the receiver.
Coupling is affected by:
- distance
- alignment
- coil size
- coil shape
- orientation
- magnetic materials
- surrounding objects
Better coupling generally improves energy transfer.
Coupling Coefficient
The degree of coupling between two coils can be described using the coupling coefficient, k.
Its value ranges approximately from:
0 ≤ k ≤ 1
A value close to 1 represents very strong coupling.
A small value represents weak coupling.
Mutual inductance is related to coupling by:
M = k√(L₁L₂)
where:
- M = mutual inductance
- k = coupling coefficient
- L₁ = transmitter inductance
- L₂ = receiver inductance
Better coil alignment and smaller separation can increase k.
Mutual Induction
The transmitter and receiver interact through mutual induction.
If current in the transmitter coil changes, an EMF is induced in the receiver.
For a simplified system:
|ε₂| = M|ΔI₁/Δt|
where:
- ε₂ = induced EMF in receiver
- M = mutual inductance
- ΔI₁/Δt = rate of change of transmitter current
Greater mutual inductance can therefore increase the induced voltage for the same rate of current change.
Why Alternating Current Is Used
Suppose direct current flows steadily through the transmitter coil.
After the initial change:
current becomes constant
↓
magnetic field becomes approximately constant
↓
magnetic flux becomes approximately constant
↓
no sustained induced EMF
Wireless charging therefore requires a changing current rather than steady DC in the transmitter coil.
In practical systems, electronics often convert DC from a power supply into high-frequency alternating or switching current.
Frequency
Wireless charging systems commonly operate using rapidly changing currents.
Higher frequency means the magnetic field changes more rapidly.
From Faraday's law:
|ε| = N|ΔΦ/Δt|
a more rapidly changing magnetic flux can help produce a larger induced EMF.
However, frequency cannot simply be increased without limit because higher frequencies can also increase:
- electrical losses
- heating
- electromagnetic interference
- circuit-design challenges
Engineers select an appropriate operating frequency for the system.
Resonant Wireless Power Transfer
Some wireless power systems use resonance.
Both transmitter and receiver can contain inductors and capacitors that form resonant circuits.
The resonant frequency is approximately:
f₀ = 1/(2π√(LC))
If the transmitter and receiver are tuned appropriately, energy transfer can become more effective.
This is called resonant inductive coupling.
Why Resonance Helps
A resonant circuit naturally responds strongly near its resonant frequency.
If the transmitter and receiver are tuned to compatible frequencies:
- oscillating currents can become stronger
- magnetic energy exchange can become more effective
- useful power transfer may occur with weaker coupling than in simple inductive systems
Resonance can therefore help extend the useful operating range or improve transfer under suitable conditions.
Energy in the Magnetic Field
An inductor stores energy in its magnetic field.
The energy stored is:
E_L = ½LI²
During wireless power transfer, magnetic fields act as part of the mechanism carrying energy between the transmitter and receiver systems.
The energy ultimately comes from the electrical power source.
Wireless charging does not create energy.
Efficiency
Wireless charging efficiency can be calculated using:
efficiency = P_output/P_input × 100%
where:
- P_input = electrical power supplied to the transmitter system
- P_output = useful electrical power delivered to the receiving system
Real wireless charging systems always have some energy losses.
Worked Example: Charging Efficiency
A wireless charger receives:
P_input = 20 W
The device receives:
P_output = 16 W
Efficiency:
efficiency = 16/20 × 100%
efficiency = 80%
Power lost:
P_loss = 20 − 16
P_loss = 4 W
This lost energy is mainly converted into thermal energy in various parts of the system.
Worked Example: Useful Power
A wireless charging system receives:
P_input = 50 W
and operates at:
90% efficiency.
Useful output power:
P_output = 0.90(50)
P_output = 45 W
Power lost:
50 − 45
P_loss = 5 W
Worked Example: Input Power
A receiver requires:
P_output = 12 W
The wireless system is:
75% efficient.
Using:
0.75 = 12/P_input
P_input = 12/0.75
P_input = 16 W
Therefore, the system must receive 16 W to deliver 12 W usefully.
Factors Affecting Charging Efficiency
Wireless power efficiency can depend on many factors.
Important factors include:
- coil alignment
- coil separation
- coil size
- number of turns
- coil resistance
- operating frequency
- resonant tuning
- magnetic coupling
- surrounding materials
- power electronics
- heating losses
Engineers optimize these factors together rather than changing only one variable.
Coil Resistance
Real coils have electrical resistance.
When current flows through a coil:
P_loss = I²R
Some electrical energy therefore becomes thermal energy.
Using conductors with appropriately low resistance can help reduce these losses.
Eddy-Current Losses
Changing magnetic fields can induce unwanted eddy currents in nearby conductive objects.
These currents can cause heating.
For example, a metal object placed unintentionally near a powerful wireless charging system could absorb electromagnetic energy.
Practical systems therefore use:
- shielding
- object detection
- power control
- careful coil design
to manage unwanted heating.
Magnetic Materials
Magnetic materials can be used to help direct magnetic flux.
For example, ferrite materials may be placed behind charging coils.
They can help:
- guide magnetic flux
- improve coupling
- reduce unwanted fields
- improve system performance
Material selection is therefore an important part of wireless charger design.
Heating
Wireless charging systems can become warm because of:
- resistance in coils
- losses in electronics
- eddy currents
- battery charging losses
- imperfect magnetic coupling
Excessive temperature can reduce efficiency and may shorten battery or component life.
Modern charging systems therefore monitor and manage temperature.
Charging a Battery
The receiver coil does not normally connect its raw alternating output directly to a battery.
The received electrical energy must be processed.
A simplified pathway is:
receiver coil
↓
induced AC
↓
rectifier
↓
DC
↓
voltage/current regulation
↓
battery charging system
↓
battery
This ensures that the battery receives electrical energy under appropriate conditions.
Rectification
A rectifier converts alternating current into direct current.
This is important because batteries are charged using controlled DC.
Therefore, wireless charging involves both electromagnetic induction and electronic power conversion.
Control and Communication
Modern wireless charging systems often contain control electronics.
The transmitter and receiver may exchange information about:
- required power
- charging state
- temperature
- alignment
- detected objects
- fault conditions
The transmitter can then adjust its output.
Wireless charging is therefore more sophisticated than simply placing two coils beside each other.
Smartphones
Wireless smartphone charging is one of the most familiar applications.
The charging pad contains a transmitter coil.
The phone contains a receiver coil.
When positioned correctly:
charging pad → changing magnetic field → phone receiver coil → electrical power → battery
This eliminates the need to insert a charging connector each time.
Wearable Devices
Wireless charging is particularly useful for:
- smartwatches
- fitness trackers
- wireless earbuds
- other compact wearable electronics
These devices may benefit from having fewer exposed electrical contacts.
Wireless charging can make devices easier to seal against:
- moisture
- dust
- dirt
Electric Toothbrushes
Electric toothbrushes have used inductive charging for many years.
Because charging can occur without exposed electrical contacts, the device can be designed with a sealed outer casing.
This is useful for equipment regularly used around water.
Medical Applications
Wireless power can be valuable in some medical technologies.
Potential applications include powering or charging:
- implanted devices
- sensors
- specialized medical electronics
Reducing the need for physical electrical connections can be useful when devices must remain sealed or are difficult to access.
Medical wireless-power systems require particularly careful control and safety engineering.
Electric Vehicles
Wireless power transfer can also be used to charge electric vehicles.
A transmitter system can be installed in or near a parking surface.
A receiver is mounted underneath the vehicle.
The basic pathway is:
electrical grid
↓
power electronics
↓
ground transmitter coil
↓
changing magnetic field
↓
vehicle receiver coil
↓
power electronics
↓
battery
Vehicle Alignment
Coil alignment is especially important for vehicle charging.
If the vehicle is parked incorrectly:
- coupling can decrease
- efficiency can fall
- charging power can decrease
Systems may therefore use:
- parking guidance
- sensors
- multiple coils
- automatic alignment assistance
to improve coupling.
Dynamic Wireless Charging
A more advanced concept is dynamic wireless charging.
Instead of charging only while parked, transmitter systems could be installed along a roadway.
A moving vehicle could receive electrical energy while travelling.
Potential benefits include:
- extended driving range
- reduced dependence on stationary charging
- potentially smaller batteries in some applications
However, such systems require extensive and costly infrastructure.
Industrial Applications
Wireless power transfer can be useful in industrial systems where physical electrical contacts are inconvenient.
Examples can include:
- rotating machinery
- automated guided vehicles
- warehouse robots
- factory sensors
- sealed equipment
- equipment operating in dusty or wet environments
Removing exposed electrical contacts can reduce some maintenance problems.
Rotating Systems
Supplying electrical energy to a rotating component can be difficult because ordinary wires would twist.
Traditional systems may use:
- slip rings
- brushes
Wireless power transfer provides another possibility.
A stationary transmitter can transfer energy magnetically to a rotating receiver without continuous mechanical electrical contact.
Advantages of Wireless Charging
Wireless charging can offer several advantages:
- convenient charging
- no repeated connector insertion
- fewer exposed electrical contacts
- easier sealing against water and dust
- reduced connector wear
- automated charging
- useful operation with rotating or moving systems
- potential charging of difficult-to-access devices
These advantages can make wireless power particularly useful in specialized environments.
Limitations of Wireless Charging
Wireless power transfer also has disadvantages.
These may include:
- lower efficiency than a well-designed wired connection
- energy losses as heat
- limited transfer distance
- sensitivity to alignment
- additional electronic components
- greater system cost
- electromagnetic interference concerns
- possible unwanted heating of nearby conductive objects
- limits on power-transfer rate in some systems
The advantages must therefore be weighed against the costs and losses.
Wired vs Wireless Charging
| Wired Charging | Wireless Charging |
|---|---|
| Direct electrical connection | Energy transferred electromagnetically |
| Usually strong electrical coupling | Magnetic coupling depends on geometry |
| Often highly efficient | Can have additional coupling losses |
| Requires connectors | No exposed charging connector required |
| Less sensitive to position | Often sensitive to coil alignment |
| Can be simple and inexpensive | Requires coils and control electronics |
| Connector can wear | Reduced connector wear |
| Cable must be physically connected | Greater convenience and automation |
Wireless charging is therefore not automatically superior. Its value depends on the application.
Why Wireless Charging Is Not Truly "Energy Through Nothing"
The transmitter and receiver do not need electrical contact, but energy is still transferred through an electromagnetic field.
The energy does not disappear from one location and magically appear in another.
The process follows electromagnetic laws and conservation of energy:
source electrical energy → electromagnetic field → receiver electrical energy + losses
Wireless Power and Distance
A common misconception is that ordinary wireless chargers can efficiently transmit large amounts of power over arbitrary distances.
Magnetic coupling generally decreases rapidly as the coils move farther apart.
Therefore, most inductive charging systems operate over relatively short distances.
Resonant systems can improve useful transfer under weaker coupling, but they do not eliminate the fundamental engineering challenges associated with distance.
Improving Wireless Charging Efficiency
Engineers can improve efficiency by:
- aligning coils carefully
- reducing unnecessary separation
- optimizing coil dimensions
- reducing coil resistance
- using suitable operating frequencies
- using resonant tuning
- adding magnetic flux-guiding materials
- improving power electronics
- detecting foreign objects
- managing temperature
Efficient wireless charging depends on the complete system.
Worked Example: Energy Delivered
A wireless charger delivers:
P_output = 15 W
for:
t = 30 minutes
Convert time:
30 min = 1800 s
Energy:
E = Pt
E = (15)(1800)
E = 27,000 J
or:
E = 27 kJ
Worked Example: Including Efficiency
Suppose the charger delivers:
27 kJ
to the device and is:
75% efficient.
Input energy:
E_input = 27/0.75
E_input = 36 kJ
Energy lost:
36 − 27
E_loss = 9 kJ
Wireless Power and Resonance
Consider two resonant circuits tuned to the same frequency.
If:
f_transmitter ≈ f_receiver
energy transfer can be enhanced.
If the receiver is poorly tuned:
f_transmitter ≠ f_receiver
the response can become weaker.
This shows why resonance is useful in some wireless-power designs.
Comparing Transformers and Wireless Charging
| Transformer | Wireless Power System |
|---|---|
| Primary and secondary coils | Transmitter and receiver coils |
| Mutual induction | Mutual induction |
| Changing magnetic flux | Changing magnetic flux |
| Often tightly coupled | Often more loosely coupled |
| Usually common magnetic core | Often separated by air gap |
| Designed for efficient voltage transformation | Designed for contactless power transfer |
The underlying electromagnetic principles are closely related.
Energy Conservation
Suppose a wireless charger receives:
100 J
of electrical energy.
If it operates at:
85% efficiency
then:
Useful output = 85 J
Energy lost = 15 J
The lost energy has not disappeared.
It has been transferred mainly into unwanted thermal energy and other losses.
Therefore:
E_input = E_useful + E_losses
Wireless power transfer obeys conservation of energy like every other electrical system.
A Complete Wireless Charging Problem
A wireless charging pad receives:
P_input = 25 W
The system operates at:
88% efficiency.
Useful power:
P_output = 0.88(25)
P_output = 22 W
Power loss:
P_loss = 25 − 22
P_loss = 3 W
If the charger operates for:
20 minutes
then:
t = 1200 s
Useful energy transferred:
E = Pt
E = (22)(1200)
E = 26,400 J
or:
E = 26.4 kJ
Designing a Wireless Charging System
An engineer designing a wireless charging system must consider:
- required power
- transmitter coil size
- receiver coil size
- coil separation
- alignment
- operating frequency
- mutual inductance
- resonant frequency
- resistance
- efficiency
- heating
- electromagnetic interference
- control electronics
- safety
- cost
Wireless charging is therefore an application of several interconnected physics concepts.
Connections to Other Electromagnetic Topics
Wireless power transfer combines many ideas:
Electromagnetic induction
Changing flux induces EMF.
Mutual inductance
Changing current in one coil produces effects in another.
Transformers
Energy moves between magnetically coupled coils.
LC resonance
Tuned circuits can improve energy transfer.
Eddy currents
Unwanted induced currents can produce heating losses.
Energy conservation
Useful output energy must come from the input electrical supply.
Wireless charging is therefore an excellent real-world application of electromagnetic induction.
Common Mistakes
Thinking wireless charging transfers electricity directly through the air
Energy is transferred through changing electromagnetic fields, which induce electrical effects in the receiver.
Thinking a steady DC current is sufficient
Continuous induction requires changing magnetic flux.
Thinking the two coils must touch
The coils can be physically separated because they are magnetically coupled.
Thinking distance does not affect charging
Increasing separation generally reduces magnetic coupling and efficiency.
Ignoring coil alignment
Poor alignment can reduce flux linkage and charging performance.
Thinking wireless charging is always more efficient than wired charging
Wireless systems can have additional electromagnetic and conversion losses.
Thinking resonance creates energy
Resonance can improve energy transfer, but it does not create energy.
Thinking all lost energy disappears
Most losses eventually become thermal energy.
Thinking wireless charging only works for phones
Applications range from tiny electronics to vehicles and industrial equipment.
Key Terms
Wireless power transfer — transfer of electrical energy without a direct conductive electrical connection.
Wireless charging — use of wireless power transfer to supply energy to a device or battery.
Transmitter coil — coil that produces the changing magnetic field used to transfer energy.
Receiver coil — coil in which an EMF is induced by the transmitter's changing magnetic field.
Electromagnetic induction — production of EMF due to changing magnetic flux.
Mutual induction — induction in one circuit caused by changing current in another circuit.
Mutual inductance — measure of the electromagnetic coupling between two circuits.
Magnetic coupling — degree to which magnetic flux produced by one coil links another coil.
Coupling coefficient — quantity describing the strength of coupling between two inductors.
Resonant inductive coupling — wireless energy transfer using magnetically coupled circuits operating near resonance.
Rectifier — circuit that converts AC into DC.
Efficiency — proportion of input power or energy transferred as useful output.
Eddy current — circulating current induced within a conductor by changing magnetic flux.
Ferrite — magnetic material often used to guide magnetic flux while limiting eddy-current losses.
Foreign-object detection — system used to identify nearby objects that could absorb energy and heat undesirably.
Dynamic wireless charging — wireless transfer of energy to a vehicle or device while it is moving.
Key Takeaways
- Wireless charging transfers electrical energy without a direct conductive connection.
- Inductive wireless charging is based on electromagnetic induction.
- Alternating current in the transmitter coil creates a changing magnetic field.
- The changing magnetic field produces changing magnetic flux through the receiver coil.
- Changing magnetic flux induces an EMF in the receiver.
- The receiver's electrical output is processed before being used to charge a battery.
- Wireless charging resembles a transformer with more loosely coupled coils.
- Mutual inductance describes the interaction between transmitter and receiver coils.
- Coil alignment strongly affects magnetic coupling.
- Increasing separation generally reduces coupling and charging efficiency.
- Coil geometry, resistance, frequency, materials, and power electronics also affect efficiency.
- Resonant circuits can improve energy transfer under suitable conditions.
- Wireless charging systems still obey conservation of energy.
- Energy losses commonly appear as unwanted heating.
- Wireless charging offers convenience, reduced connector wear, and easier sealing of devices.
- Its limitations include losses, short transfer distances, alignment requirements, heating, and added system complexity.
- Wireless power is used in phones, watches, earbuds, toothbrushes, medical equipment, industrial systems, and electric vehicles.
- Wireless vehicle charging can be stationary or, in more advanced systems, dynamic.
- Wired charging may remain preferable where maximum efficiency, simplicity, or high power transfer is the main priority.
- Wireless power transfer combines electromagnetic induction, mutual inductance, resonance, electronics, and energy conservation in a practical technology.
Check Your Understanding
- Explain how a transmitter coil transfers energy to a receiver coil without direct electrical contact.
- Why must the magnetic field produced by the transmitter change with time?
- State Faraday's law and explain how it applies to a wireless charger.
- Explain why wireless charging can be compared with transformer operation.
- Describe how poor alignment between transmitter and receiver coils affects charging efficiency.
- Explain why increasing the distance between the coils usually decreases useful power transfer.
- A wireless charger receives 30 W and delivers 24 W to a device. Calculate its efficiency.
- A wireless charging system is 80% efficient and must deliver 40 W to a receiver. Calculate the required input power.
- Explain how coil resistance causes energy loss in a wireless charging system.
- What is resonant inductive coupling, and why can resonance improve wireless power transfer?
- Explain why the AC induced in a receiver coil normally needs to be rectified before charging a battery.
- Compare wireless charging with wired charging in terms of convenience, efficiency, alignment, physical wear, and system complexity.
- Describe three applications of wireless power transfer other than smartphone charging and explain why wireless transfer is useful in each.
- Explain how unwanted eddy currents could reduce efficiency or cause a safety problem in a wireless charging system.
- An engineer is designing a wireless charging system for an electric vehicle. Explain how coil alignment, coil separation, operating frequency, resonance, mutual inductance, resistance, thermal losses, and control systems should be considered when designing an efficient system.