Thane C. Heins Ottawa ON thaneh@potentialdifference.ca 613.293.1131

1. INCLUDING
THE WORK ENERGY PRINCIPLE
INTO
LENZ'S LAW OF INDUCTION
(Generator Armature Reaction)
MATHEMATICALLY PROVES THAT
ELECTRIC GENERATORS
CANNOT
VIOLATE THE WORK-ENERGY PRINCIPLE
AS CLAIMED BY THE GLOBAL SCIENTIFIC COMMUNITY
AND WHY
THIS PROCESS ALSO PROVES
THAT ENERGY CAN BE CREATED
Thane C. Heins Chairman Co-Founder and CTO, Potential Difference Inc.

2. Abstract
The current scientific explaination of Generator Armature Reaction as provided in Lenz's Law of Induction
incorrectly claims that all electric generators have the ability to violate the Work-Energy Principle and
perform Negative Work without Energy.
The primary objective of this paper is to prove that Generator Armature Reaction and Lenz's Law of
Induction both refer to Negative Work and that this Negative Work and all Work requires an Energy Source
as specified by the Work-Energy Principle.
The secondary objective is to explain what this Energy Souce is how it is Created.
The third objective is to show how all electric generators exceed 100% efficiency when the Energy required
to perform this Negative Work is factored in and no longer ignored.
And finally, to explain that when this Energy is delayed sufficiently in the Time Domain as with the US
patented ReGenX Generator the Created Energy which currently performs Negative Work can now be used
to perform Positive Work.
When this transition occurs the efficiency of an electric generator can reach Infinite Efficiency.
Index Terms—Electric Generator, Electric Generator Efficiency, Lenz's Law, Newtonian Mechanics, Electricity and
Magnetism, Energy, Work, Power, Torque, Electric Vehicle (EV), Work-Energy Principle, Universe, Isolated
System, Closed System, Open System, Infinite System, Infinite Efficiency
Introduction
This paper involves the inclusion of the Work-Energy Principle into Lenz's Law of Induction. This s has an
important benefit with regards to advancing our understanding of the subject of Electric Generator
Performance, Electricity and Magnetism, the Nature of Electromagnetically Induced Magnetic Fields, Work,
Energy, Newtonian Mechanics, and the Physical Structure of the Universe.
Sir Issac Newton formulated the subject of Newtonian Dynamics in terms of the 3 Laws of Motion. Lenz's Law
has been used by physicists since 1822 to explain how Newton's 3rd
Law is expressed in electricity generation
and specifically with regards to electric generator performance.
More recently Newton's 3rd
Law is employed colloquially in the explanation of electric vehicle regenerative
braking – whereby an electric vehicle's kinetic energy is reduced when it is converted to electrical energy and
stored in an electric vehicle's battery.

3. We can state Newton's Laws effectively, as follows:
Law I: Every body of mass (M) perseveres in its state of rest, or of uniform motion in a right line, unless it is
compelled to change that state by forces (F) impressed thereon.
Law II: The alteration of motion of said body is ever proportional to the motive force (M) impressed on the
body; and is made in the direction of the right line in which that force (F) is impressed. A body of mass (M)
when acted on by a force (F) accelerates with an acceleration (A) such that F = MA.
Law III: To every action there is always an equal and opposed reaction; a force (F) acting on a body of mass (M)
will be accompanied somewhere by an equal and opposite reactive force (−F). [1] Newton's Second Law states
that the acceleration of an object is proportional to the force acting on it, and inversely proportional to its
mass. This law can be used to help demonstrate the Law of Conservation of Energy, which states that energy
cannot be created or destroyed in an isolated system, that the total energy of an isolated system remains
constant over time.
In an isolated system, neither matter nor energy transfer between a system and its surroundings are allowed.
The current widely accepted understanding of our universe is that it is an isolated system, because it contains
everything by definition, and thus there can be no exchange of energy with anything. If there could be, it would
be counted within the universe. [2] Within our known “isolated” universe and within all the laws of physics
with which we use to describe it, the overriding principle states that, no creation of energy and no destruction
of energy is allowed.
The Work-Energy Principle's inclusion into Lenz's Law of Induction provides us with a very important
contribution to the continued expansion of our understanding of the relationship between Energy and Work
and the physical structure of our universe. How energy is the currency required to perform work in our infinite
and ever expanding albeit isolated universe.
It is universally accepted that an electric generator is a machine which converts mechanical input energy to
electrical output energy. The current accepted explanation of electric generator performance is provided by
several laws of physics, including Faraday's Law of Induction, Lenz's Law of Induction, Newton's Third Law, and
the Law of Conservation of Energy which all work in concert to provide an explanation of the relationship
between the magnitude of mechanical input energy and its conversion to electrical output and the process
involved.
According to Faraday's Law, whenever the flux threading through or linking with a closed circuit is changed, an
electromotive force (EMF or voltage) is induced which causes a current to flow in the circuit. the direction of

4. the induced current has a definite relation to the variation of the field that produces it.
This relation is formalized by Lenz's Law of Induction, which may be stated as follows:
An induced EMF will cause a current to flow in a closed circuit in such a direction
that its magnetic effect will oppose the change that produces it.
This rule follows directly from the Law of Conservation of Energy: that is to cause an induced current to flow
requires the expenditure of energy. In the case of a generator, for example, when the induced current is caused
to flow through a load connected to the generator, electric energy is expended. The field produced by the
current is always in a direction so that it reacts with the main generator field, to oppose the turning action of
the prime mover driving the generator.
Thus, the greater the electric energy supplied to the load, the greater is the reaction and in turn the greater is
the mechanical energy required from the prime mover. Energy must be supplied to the generator at the same
rate that it is being taken from the generator. [3]
In physics and chemistry, the Law of Conservation of Energy states that the total energy of an isolated system
remains constant; it is said to be conserved over time. This law, means that energy can neither be created nor
destroyed; rather, it can only be transformed or transferred from one form to another.
For instance, chemical energy is converted to kinetic energy when a stick of dynamite explodes. If one adds up
all forms of energy that were released in the explosion, such as the kinetic energy and potential energy of the
pieces, as well as heat and sound, one will get the exact decrease of chemical energy in the combustion of the
dynamite. [4]
In physical science, an isolated system is either of the following: a physical system so far removed from other
systems that it does not interact with them. A thermodynamic system enclosed by rigid immovable walls
through which neither mass nor energy can pass. This can be contrasted with what (in the more common
terminology used in thermodynamics) is called a closed system, being enclosed by selective walls through
which energy can pass as heat or work, but not matter; and with an open system, which both matter and
energy can enter or exit, though it may have variously impermeable walls in parts of its boundaries. An isolated
system obeys the conservation law that its total energy–mass stays constant. Most often, in thermodynamics,
mass and energy are treated as separately conserved. [2]

5. Our universe is considered to be by definition of the word isolated, because it contains everything and thus
there can be no exchange of energy with anything and no creation of energy. If there could be, it would be
counted within the universe.
Figure 1.0 Examples of Isolated, Closed and Open Systems
Figure 2.0 Example of a Closed System
Electric generators are accepted as being closed systems which include an energy input and an energy output.
In electric generator operation it is accepted that mechanical energy is the input and electrical energy is the
output.
Heat and noise are other energy conversion outputs but because they are unintended consequences they are
commonly referred to as losses in the system. Joule heating, also known as resistive, resistance, or Ohmic
heating, is the process by which the passage of an electric current through a conductor produces heat. Joule's
first law, also known as the Joule–Lenz law, states that, the power of heating generated by an electrical
conductor is proportional to the product of its resistance and the square of the current:
P = I^2 R

6. Joule heating is referred to as ohmic heating or resistive heating because of its relationship to Ohm's Law. It
forms the basis for the large number of practical applications involving electric heating. [10] Resistors create
electrical noise, called Johnson–Nyquist noise. There is an intimate relationship between Johnson–Nyquist
noise and Joule heating, explained by the fluctuation-dissipation theorem.[5] If electric current is running
through a wire loop with a resistor in it, the current will rapidly go to zero because of the resistance. Resistance
dissipates electrical energy, turning it into heat (Joule heating). [6]
If one adds up all forms of energy that were released in a generator's conversion of mechanical to electrical
energy and the energy converted to heat and sound, one will get the exact decrease of mechanical input
energy. This mechanical input energy decrease must be compensated with a mechanical energy input increase
from the prime mover if the kinetic energy of the prime mover generator system is to be maintained
In physics, energy is the quantitative property that must be transferred to an object in order to perform work
on, or to heat, the object. Energy is considered to be a conserved quantity; the Law of Conservation of Energy
states that,
Energy can be converted in form, but not created or destroyed. [8]
A quantitative property is a property of a physical system which exists in a range of values corresponding with a
number, such that the system can be described as having a particular number of a unit of measurement of that
property. [7]
Lenz's Law is also referred to as Motor Action in a Generator. Motor Action in a Generator occurs when the
prime mover is rotating the generator in a clockwise direction for example, and the electromagnetic fields set
up by the induced currents in the armature windings attempt to drive the generator as a motor in a
counterclockwise direction. This tendency to oppose the prime mover is called Motor Action in a Generator.
The higher the current in the armature windings, the
stronger the motor action. [7] Motor Action in a
Generator is also often referred to as:
• Generator Armature Reaction
• Counter Electromagnetic Torque
• Magnetic Effect
• Electric Vehicle Regenerative Braking
Figure 3.0 Motor Action in a Generator

7. Motor Action in a Generator is a counter electromagnetic torque which performs negative work against the
torque direction supplied by the prime mover. The result is additional input power must be supplied to the
generator by the prime mover if the system kinetic energy is to be maintained.
Motor Action in a Generator, or the Reaction (physics) [11] is described by the third of Newton's Laws of
Motion of classical mechanics, all forces occur in pairs such that if one object exerts a force on another object,
then the second object exerts an equal and opposite reaction force on the first.
Newton's third law is also more generally stated as:
"To every action there is always opposed an equal reaction”
Or the mutual actions of two bodies upon each other are always equal, and directed to contrary parts. The
attribution of which of the two forces is the action and which is the reaction is arbitrary. Either of the two can
be considered the action, while the other is its associated reaction. [1]
As stated previously, the electromagnetic field produced by the current is always in a direction so that it reacts
with the main generator field, to oppose the turning action of the prime mover driving the generator. Thus, the
greater the electric energy supplied to the load, the greater is the reaction and in turn the greater is the
mechanical energy required from the prime mover. Energy must be supplied to the generator at the same rate
that it is being taken from the generator. [3]
If additional energy is not supplied to the prime mover and if no additional mechanical energy is supplied to the
generator's drive shaft at the same rate it is being taken from the generator, the Counter Electromagnetic
Torque produced inside the generator will reduce the kinetic energy of the prime mover and the generator's
electrical output will drop to an undesired level.
In electric vehicle operation, motor action in a generator aka regenerative braking will decelerate the electric
vehicle causing a reduction in the kinetic energy of the electric vehicle as the battery recharging drops
simultaneously.
In US mechanical engineering, torque is defined mathematically as the rate of change of angular momentum of
an object (in physics it is called "net torque"). The definition of torque states that one or both of the angular
velocity or the moment of inertia of an object are changing. Moment is the general term used for the tendency
of one or more applied forces to [perform work] and rotate an object about an axis, (the concept which is
called torque in physics). For example, a rotational force applied to a shaft causing acceleration, such as a drill
bit accelerating from rest, results in a moment called a torque. If a torque is allowed to act through a rotational
distance, it is doing work. [8] The work being performed by the torque increases the kinetic energy of the drill

8. bit.
Work transfers energy from one place to another, or one form to another. Work is closely related to energy.
[12]
The Work-Energy Principle states that:
An increase in the Kinetic Energy of a rigid body is caused by an equal amount of Positive Work done on the
body by the resultant force acting on that body. Conversely, a decrease in Kinetic Energy is caused by an
equal amount of Negative Work done by the resultant force. [9]
Motor Action in a Generator, Generator Armature Reaction, Counter Electromagnetic Torque, Magnetic Effect
and Electric Vehicle Regenerative Braking all refer to the exact same thing.
They all refer to the Kinetic Energy reduction effect that the generator has on the prime mover and or the
deceleration produced on an electric vehicle when mechanical input energy is being converted to electrical
output energy.
The Work-Energy Principle states that,
All Work refers to an activity involving a Force and Movement in the direction of the force.
Energy is the capacity for doing work.
You must have energy to accomplish work - it is like the "currency" required for performing work.
For example, in order to do 100 joules of work, you must expend 100 joules of energy.
Power is the rate of doing work or the rate of using energy, which are numerically the same.
If you do 100 joules of work in one second (using 100 joules of energy), the power is 100 watts. [9]
The Work-Energy Principle mathematically ensures that if we want to increase the Kinetic Energy of an electric
vehicle or accelerate it from an initial Kinetic Energy level to a higher Kinetic Energy level within a specified

9. time interval, we must perform a certain amount of Positive Work on that vehicle. The Work-Energy Principle
also ensures we must expend a certain amount of Energy in the process because energy is the currency
required to perform that Positive Work.
Conversely if we want to decrease the Kinetic Energy of an electric vehicle or decelerate it from an initial
Kinetic Energy level to a lower Kinetic Energy level, within an identical time interval as above we must perform
an identical amount of Negative Work on that vehicle. The Work-Energy Principle also ensures we must
expend a certain amount of Energy in the process because Energy is the currency required to perform that
Negative Work.
If all the parameters in the electric vehicle example above are the exactly the same then we can
mathematically quantify the exact energy expenditure required to perform the positive work, during
acceleration while increasing the vehicle's kinetic energy. Similarly we can also quantify the exact energy
expenditure required to perform the negative work, during deceleration while reducing the vehicle's kinetic
energy.
In electric vehicle operation it is universally accepted that the energy required to accelerate the electric vehicle
and increase its kinetic energy is provided by the chemical energy which is stored in the electric vehicle's
battery and its conversion to electrical energy which is consumed by the electric vehicle's electric motor. In
electric power generation it is also universally accepted that the energy required to maintain the kinetic energy
of the generator when current is being supplied to the load is provided by the prime mover and the input
energy source which powers the prime mover.
The questions this paper wishes to explore and answer is:
1) What is the energy source which is required to produce the negative work performed during deceleration
of the electric vehicle, when the vehicle's kinetic energy is reduced?
2) What is the energy source required for the generator to perform the negative work against the prime
mover, reducing its kinetic energy and necessitating a prime mover input increase as described previously in
“motor action in a generator?”
3) And where does this energy come from?
And more specifically - what is the energy source which is required to produce the counter electromagnetic
torque and the rate of change of angular momentum or "net torque reduction" of an electric vehicle's drive
shaft or a prime mover's drive shaft which is connected to an electric generator under load?

10. As provided previously, the definition of torque states that, one or both of the angular velocity or the moment
of inertia of an object are changing – and an identical increase (Positive Work) or decrease (Negative Work) in
the angular velocity or the moment of inertia of an object will require the exact same magnitude of energy.
Moment is the general term used for the tendency of one or more applied forces to [perform work] and rotate
an object about an axis, (the concept which is called torque in physics).[8]
Inclusion of the Work-Energy Principle and expansion of Lenz's Law of Induction will provide the answers
required and this process will allow us to quantify the source of the energy required to perform this negative
work or kinetic energy reduction in electric power generation and electric vehicle operation.
Once again Lenz's Law states that, an induced EMF will cause a current to flow in a closed circuit in such a
direction that its magnetic effect will oppose the change that produces it. [3]
“Magnetic effect” refers to the electromagnetic field created around the current bearing wires inside the
generator which make up the generator coil.
“Oppose” means to actively resist or work against the rotating magnetic field which is responsible for initiating
the “change that produces” the induced EMF and current in the first place.
The resultant effect is the production of a Counter Electromagnetic Torque and Negative Work being
performed and a reduction in the Kinetic Energy or deceleration of the electric vehicle and a reduction in the
Kinetic Energy of the prime mover in electric power generation.
Electric vehicle regenerative braking and Motor Action in a Generator both refer to Negative Work being
performed and system Kinetic Energy Reduction.
The Energy Source required to perform this negative work in both cases is the induced Electromagnetic Field
Energy which is being created around the current bearing wires inside the generator.
Therefore; Lenz's Law of Induction can be rewritten as follows,
An induced EMF will cause a current to flow in a closed circuit in such a direction that the
Electromagnetic Field Energy created will perform Negative Work and oppose the change that produces it.
In the case of a generator, for example, when the induced current is caused to flow through a load connected
to the generator, electric energy is expended is expended in the load.
The electromagnetic field energy created by the current is always in such a direction that it produces a counter
electromagnetic torque such that it reacts with the generator's rotating magnetic field, it reduces the torque

11. supplied by the prime mover.
The counter electromagnetic torque performs negative work in opposing the turning action of the prime mover
driving the generator. Thus, the greater the electric energy supplied to the load, the greater is the reaction and
in turn the greater is the mechanical energy required from the prime mover.
Energy must be supplied to the generator at the same rate that it is being created inside the generator by the
electromagnetic field energy and at the same rate this created energy is performing negative work if the kinetic
energy of the system is to be maintained and not allowed to decrease.
In electric vehicle operation the created electromagnetic field energy will perform negative work on the
electric vehicle's drive shaft and it will reduce the kinetic energy of the vehicle when electric recharge current is
being supplied to the electric vehicle's battery.
Inclusion of the Work-Energy Principle into Lenz's Law of Induction introduces the Law of Creation of Energy
and it also introduces a new Energy System – an Infinite System where energy is being created over time.
Figure 4.0 Example of an Infinite System
In physics, the Law of Creation of Energy states that the total energy of an Infinite System; is said to be created
and increased over time.
This law, means that energy can and is being created and it can also be transformed or transferred from one
form to another. For instance, if one adds up all forms of energy that were transformed in the generation of
electricity or the conversion of mechanical input energy to electrical output energy, as well as the heat and

12. sound energy and the electromagnetically created energy which performs the negative work or kinetic energy
reduction one will get the exact magnitude of the energy created.
The Law of Creation of Energy is a new law of physics, another is Heins' Law of Induction and Heins-Newton's
4th
Law of Motion.
The Law of Creation of Energy explains how negative work is being performed inside all electric generators by
electromagnetic field energy that is created when electric power is delivered to a load and how this energy can
be quantified.
Heins Law explains how this very same created electromagnetic field energy – when delayed sufficiently in the
time domain can now be used to perform positive work, system kinetic energy increase during electricity
generation and why mechanical input energy is no longer required during electricity generation.
Heins Law explains how electric generators can now be made to operate at infinite efficiency by eliminating
mechanical input energy requirement during electricity generation.
Heins-Newton's 4th
Law of Motion states that,
When an electric generator's electric current is delayed sufficiently in the time domain,
the created electromagnetic field energy will produce an equal and complementary reaction.
This equal and complementary reaction manifests itself as a Complementary Electromagnetic Torque
which performs positive work in the same direction as the torque supplied by the prime mover.
The kinetic energy of the prime mover is increased accordingly and the prime mover's input energy
consumption is reduced.
Heins' Law of Induction states that,
According to Faraday's Law, whenever the flux threading through or linking with a closed circuit is changed, an
electromotive force (EMF or voltage) is induced which causes a current to flow in the circuit. The timing of the
current dictates the direction of the induced current which also has a definite relation to the variation of the
field that produces it. This relation is formalized by Heins' Law of Induction, which may be stated as follows:
An induced EMF will cause a current to flow in a closed circuit.
When this current is delayed sufficiently in the time domain, the timing and direction
of the current and its magnetic effect will assist the change that produces it.

13. This rule follows directly from the Law of Creation of Energy:
That is, to cause a time delayed induced current to flow requires no expenditure of energy.
In the case of a generator, for example, when the induced current is delayed sufficiently in the time domain by
increasing the generator coil's impedance, the time delayed current is caused to flow through a load connected
to the generator, and electric energy is expended in the load.
The electromagnetic field energy created by the time delayed current and the positive work performed is
always in a direction so that it reacts with the main generator field, to assist the turning action of the prime
mover driving the generator.
Thus, the greater the electric energy supplied to the load, the greater is the reaction and in turn no mechanical
energy is required from the prime mover. Any magnitude of energy can be taken from the generator while zero
energy is required to be supplied to the generator in return because no negative work is being performed by
the generator's cretaed magnetic field energy.
Heins' Law of Induction, Heins-Newton's 4th
Law of Motion, Motor Action in a ReGenX Generator,
Complementary Electromagnetic Torque, and Infinite Electric Generator Efficiency can now all be observed in
the US patented ReGenX Generator by Potential Difference Inc.
Generator and Improved Coil Therefor Having Electrodynamic Properties US20140111054A
https://patents.google.com/patent/US20140111054A1/en
Figure 5.0 Motor Action in a ReGenX Generator
Motor action in a ReGenX Generator is a complementary electromagnetic torque which performs positive
work in the same torque direction supplied by the prime mover. The result is no additional input power must

14. be supplied to the generator by the prime mover when the generator is delivering power to the load.
Conclusion
Inclusion of the Work-Energy Principle into Lenz's Law identifies electromagnetic fields as a form of energy
which is created and which can be quantified.
The Work-Energy Principle ensures that energy is the currency required to perform both positive and negative
work. It introduces a new law of physics called the Law of Creation of Energy.
This created electromagnetic field energy produces a counter electromagnetic torque during electricity
generation which performs negative work against the turning action of the prime mover. The kinetic energy of
the prime mover in electricity generation and the kinetic energy of an electric vehicle during regenerative
braking are both reduced.
The continuous creation of electromagnetic field energy re-identifies our universe as an infinite system where
the total energy in our system is created over time.
The Law of Creation of Energy also ensures that our universe is an Infinite System where energy is being
created and exchanged continuously within it.
This new information will have an important impact on helping astronomers understand the creation and
nature of our continually expanding universe. It may be able to help explain how the kinetic energy of entire
galaxies and planets within them can expand at with an ever increasing speed.
In addition the concept that different universes may exist with potentially different laws of physics can now be
expanded to include our own universe.
The US patented ReGenX Generator delays the generator's load current in the time domain, it produces a
complementary electromagnetic torque and the negative work which is normally performed by the created
electromagnetic field energy is reversed such that positive work is performed.
This positive work negates the mechanical input power increase requirement in electric power generation and
it allows any magnitude of electricity to be generated with zero mechanical input power at infinite efficiency. In
electric vehicle operation the time delayed electromagnetic field energy that is created in the ReGenX
Generator performs positive work and it accelerates the electric vehicle while recharging its batteries – this
innovation is called Electric Vehicle Regenerative Acceleration. The more battery recharge power delivered to
the electric vehicle's batteries the faster the batteries are recharged, the more the vehicle is accelerated and
the less plug-in recharging is required.

15. References
1. https://en.wikipedia.org/wiki/Newton%27s_laws_of_motion
2. https://en.wikipedia.org/wiki/Isolated_system
3. Eugene C. Lister, Chief Electrical Engineer The Institute of Electrical and Electronics Engineers Inc.
“Lenz's Law of Induction” Electric Circuits and Machines Sixth Edition, page 85 1984
4. https://en.wikipedia.org/wiki/Conservation_of_energy
5. https://en.wikipedia.org/wiki/Fluctuation-dissipation_theorem
6. https://en.wikipedia.org/wiki/Joule_heating
7. https://en.wikipedia.org/wiki/Qualitative_property
8. …
9. https://en.wikipedia.org/wiki/Torque
10. http://hyperphysics.phy-astr.gsu.edu/hbase/work.html
11. https://en.wikipedia.org/wiki/Reaction_(physics)
12. https://en.wikipedia.org/wiki/Work_(physics)
13. https://en.wikipedia.org/wiki/Energy