Download POTENTIAL ENERGY and FIELDS

UNIT PEF
Summary Ideas
POTENTIAL ENERGY and FIELDS
Historical Perspective
Fields: The observation that some objects, like magnets, can affect other objects
without touching them was a puzzle to scientists for many hundreds of years. Early
scientists, such as Gilbert and Descartes, tried to explain such magnetic and static
electric effects using models in which streams of invisible particles or emanations
were emitted by some objects and absorbed or enveloped by others.
When developing his ideas about gravitational interactions Isaac Newton was
dissatisfied that he could not explain the observation that the Earth could attract
objects toward it without touching them. He called this phenomenon ‘action-at-adistance’ and this terminology has been used since then to describe the different
types of interaction that have this property.
In the late 18th and early 19th centuries scientists began to explain these phenomena
using an idea they called ‘spheres of influence’ or ‘lines of force’ that extended out
from objects. Finally in 1845 Michael Faraday described the idea of a magnetic field
that extended the influence of a magnet beyond its physical boundaries. So useful
was this idea that it was soon adapted to also explain the ‘action-at-distance’ nature
of static electric and gravitational interactions.
Potential Energy: Before the 19th century, scientists’ thinking about energy was
confined to what we now call kinetic energy – that is the energy associated with
motion. In this restricted sense they thought that when an object’s speed changed,
that kinetic energy was simply created or lost. However, starting around the year
1800 various scientists began to consider the temperature of objects as an indication
of another type of energy (which we call thermal energy). Carefully controlled
experiments showed that these two types of energy could be converted from one to
the other without any losses or gains, and from this the idea of the Law of
Conservation of Energy was developed.
However, for this idea to be useful, in some situations it had to be assumed that
energy could be ‘stored’ in objects, ready to be ‘released’ and transformed into more
evident types like kinetic and thermal energy. Around the middle of the 19th century
William Rankine described this ‘stored’ energy as having the potential to produce
changes in motion and temperature, and so coined the phrase potential energy to refer
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to it. This idea was quickly adopted by the scientific community because it allowed
all interactions to be described in terms of the Law of Conservation of Energy.
In the late 19th century James Clerk Maxwell used the ideas of fields and potential
energy to unify the study of electricity and magnetism into electromagnetism. In
order to do so he proposed the idea that the magnetic and electric fields could have
forms of potential energy associated with them (magnetic potential energy – MPE,
and electric potential energy – ElecPE). This idea was also adopted for use in the
description of gravitational interactions by saying the gravitational field has
gravitational potential energy (GPE) associated with it.
On the following pages we describe some of the ideas about potential energy and
fields that have been developed in this unit. They should correspond closely to ideas
used by scientists, since they are based on some of the same evidence.
Idea PEF1 – ‘Action-at-a-distance’ Interactions:
There are certain types of interaction in which the interacting objects can exert
pushes and pulls on each other even though they are not touching. These types of
interactions are known collectively as ‘action-at-a-distance’ type interactions. The
evidence for an ‘action-at-a-distance’ interaction is a change in motion without any
direct contact.
Examples are:
•
Magnetic interactions – occur between two magnets, or between a magnet
and a ferromagnetic material.
•
Static electric interactions – occur between two charged objects, or between a
charged object and an uncharged object.
•
Gravitational interactions – occur between all pairs of objects (but are only
noticeable when at least one of them is very, very, massive.)
Idea PEF2 – Accounting for ‘Action-at-a-distance’:
The phenomenon of ‘action-at-a-distance’ can be accounted for using the idea of an
invisible ‘field of influence’ that surrounds the relevant objects. Any other relevant
object that lies within that field feels its influence and is pushed or pulled
accordingly.
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Unit PEF Summary Ideas
•
Surrounding a magnet there is a
magnetic field – any other magnet,
or ferromagnetic material, within
that magnetic field, feels a push or a
pull according to how it is oriented.
The direction of the magnetic field at
any point is the direction of the force
that would be experienced by the north pole of a small test magnet at that
location. Magnetic fields point away from the North pole of magnet and
toward the South pole. The strength of the magnetic field around a magnet
gets weaker as distance from the magnet increases.
•
Surrounding
an
electric
charge (or charged object),
there is an electric field – any
other charge (or charged
object, or charges within a
neutral object) within that
electric field feels a push or a
pull according to the types of charge involved (+ or –). The direction of the
electric field at any point is the direction of the force that would be
experienced by a small positive test charge at that location. Electric fields
point away from positive charges and toward negative charges. The strength
of the electric field around a charged object gets weaker as distance from the
object increases.
•
Surrounding all objects there is a gravitational
field – any other object within that gravitational
field feels a pull toward the first object. (The
gravitational field of everyday objects is extremely
weak and usually not noticeable except under
very carefully controlled conditions. The
gravitational field of a planet is much stronger
and so shows noticeable effects.) The direction of
the gravitational field at any point is the direction of the push/pull that
would be experienced by a small mass at that location. The strength of the
gravitational field around an object gets weaker as distance from the object
increases. (However, the Earth’s gravitational field only gets weaker very
slowly as you get further and further from the Earth. You must get a few
hundred miles above the surface before the field gets much weaker.)
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Idea PEF3 – Electromagnetic Interactions:
When electric charges move through a circuit and a
compass is close by, the compass reacts by moving.
This is evidence that moving electric charges create a
magnetic field in the area around them and is the
principle on which an electromagnet works.
When a magnet moves around close to a coil of wire,
an electric current flows through the wire. This is
evidence that a moving magnet creates an electric
field in the area around it and is the principle on
which an electric generator works.
These two effects are examples of electromagnetic
interactions.
Idea PEF4 – Potential Energy:
In order that the Law of Conservation of Energy can be applied to all interactions we
assume that energy can be stored in objects/fields and that this stored energy can
increase or decrease during different types of interaction.
Idea PEF5 – Elastic Potential Energy:
When two touching objects push or pull
on each other it is possible that at least
one of them is elastic (stretchy or
compressible). In such CPP interactions
while the interacting objects are touching,
there is a change in the speed (and/or
direction) of at least one of the objects
involved
while
the
amount
of
compression or extension of at least one of
them also changes.
In order for the Law of Conservation of Energy to be used we must assume that
there is a change in the elastic potential energy (EPE) of the elastic object(s) involved.
When an elastic object gets more compressed/stretched the amount of EPE
associated with it increases, and vice versa.
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Unit PEF Summary Ideas
Idea PEF6 – Potential Energy in fields:
All types of force field store potential energy that can increase or decrease during
the relevant type of interaction. Thus the force field itself can be either an energy
giver or receiver. Using the Law of Conservation of Energy we can infer that when
the kinetic energy of the interacting objects increases, the potential energy in the
field decreases, and vice versa.
•
A magnetic field can store
magnetic potential energy (MPE)
that increases or decreases during
a magnetic interaction, if the
kinetic
energy
of
the
magnets/objects involved also
changes. When the two magnets
are attracting, the amount of MPE
in the field increases the further
apart the two magnets are.
•
An electric field can store electric
potential energy (ElecPE) that
changes during an electric charge
interaction, if the kinetic energy of
the charges/objects involved also
changes. When the two charges
are attracting, the amount of
ElecPE in the field increases the
further apart the two charges are.
•
A gravitational field can store
gravitational potential energy
(GPE) that changes during a
gravitational interaction, if the
kinetic
energy
of
the
charges/objects involved also
changes. The amount of GPE in
the field increases the further
apart the two objects are.
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Idea PEF7 – Effect of mass:
When two objects interact via an ‘action-at-a-distance’ interaction, in principle they
will both move. However, if the mass of one object is much larger than the mass of
the other, then the one with more mass will have a smaller degree of motion. In
gravitational interactions between the Earth and everyday objects (people, cars,
balls, etc), the mass of the Earth is so much larger than that of the other object
involved that the motion of the Earth is imperceptibly small.
Idea PEF8 – Gravitational Interactions on a frictionless track:
When an object is released from a certain height on a frictionless track, as it descends
the GPE in the gravitational field decreases and so the object’s KE increases (as does
the Earth’s, but imperceptibly). However, because of the Law of Conservation of
Energy the total energy (GPE+KE) involved stays constant. If the track rises again,
the object can never attain a height higher than that at which it started because that
would require more total energy than was available as GPE when it was released.
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