Physics II: Chapter 4

Reference: Beginning Physics II

Chapter 4: ELECTRIC POTENTIAL AND CAPACITANCE

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KEY WORD LIST

Conservative Force, Electric Potential Energy, Electric Potential, Equipotential Surface, Electron-Volt, Capacitance, Capacitor, Parallel Capacitors, Series Capacitors, Energy Of Capacitors, Dielectric, Polarize, Dipoles, Dielectric Constant, Permittivity

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GLOSSARY

For details on the following concepts, please consult Chapter 4.

CONSERVATIVE FORCE (Newton)
Forces, in general, are able to do work, and the work that they do can be transformed into kinetic energy. For forces that are “conservative” the work done can be expressed in terms of a change in potential energy associated with those forces. In other words, the total work done in moving a particle between two points is independent of the path taken. Equivalently, if a particle travels in a closed loop, the total work done by a conservative force is zero.

ELECTRIC POTENTIAL ENERGY (Joules)
The electric force is conservative, and work can be written in the form of a change in potential energy. The potential energy of two charges q and Q separated by a distance r is then given by:

The zero of potential energy has been chosen when r → ∞. If the charges are of the same sign, then the potential energy increases as the charges approach each other. This follows because an external force must do positive work in forcing the charges closer together against their mutual repulsion. If left to themselves, these charges would seek regions of lower potential energy.

ELECTRIC POTENTIAL (Volt = Joules/coulomb)
We could associate a specific potential energy with each point in space in a manner similar to associating an electric field to each point in space. We can view this as a situation in which the stationary charges provide each point in space with a scalar value, called the potential, V, such that the potential energy of the system will equal qV if the moving charge is at that point in space.

The unit for potential is joules per coulomb, which is the same as volt (V). The quantity ∆V is the “potential difference” between two points in the static electric field. It corresponds to the work needed per unit of charge to move a test charge between the two points. The potential is related to the potential energy in the same manner that the electric field is related to the electric force.

Voltage = Energy / charge

The relationship of electric potential to electric field is as follows:

Potential always decreases as we move along the direction in which the field points.

EQUIPOTENTIAL SURFACE
At every point there is an electric field pointing in some direction. If we move to a different point along that direction, then the potential will change. However, if we move to a different point perpendicular to that direction, the potential will not change. If we move from point to point, always in a direction perpendicular to the electric field at that point, we will sweep out a surface with all points on that surface at the same potential. This surface is called the “equipotential surface”.

A knowledge of how V varies in a region around a point allows us to obtain the magnitude and the direction of the electric field at that point.

E = -∆V/∆d

The minus sign means that E points from high to low potential.

ELECTRON-VOLT
The potential energy of any charge is given by qV, and the change in potential energy that is used in most energy related problems is ∆Up = q ∆V. A positive charge gains energy as it moves to a region of higher potential. A negative charge, such as an electron, will lose energy as it moves to a higher potential. When an electron moves through a difference of potential of one volt it gains or loses e(1) = 1.6 x 10-19 J of energy. This amount of energy is called an electron-volt, or eV. This is a very convenient unit of energy to use whenever one discusses the motion of an electron.

CAPACITANCE
Let us consider the case of two isolated conductors with charge +Q on one and -Q on the other, and a potential difference V between them. Depending on the shape of the conductors and their positions relative to each other, the charges on the conducting surfaces will distribute themselves with some definite (but not necessarily uniform) charge distribution. It is not hard to see that the potential difference V is proportional to the charge Q, as long as the geometry stays the same. We can therefore write Q = CV, and the constant C is called the capacitance of the system. This constant C = Q/V depends on the geometry of the conductors, their size, shape and position, but it does not depend on the charge on the plates. The unit for capacitance is the farad (F).

CAPACITOR
If we build a unit containing two conductors with relatively large surfaces close to each other (but not touching) we call this object a capacitor whose capacitance is C. The name derives from the fact that C represents the capacity of the two conductors to store charge on their surfaces per unit potential difference (per volt) between them. A large capacitance means that the capacitor holds a lot of charge per volt. The most common capacitor geometry is that of two close parallel, conducting plates.

The capacity of a parallel plate capacitor can be written as C = ε0A/d. Thus, doubling the area, or halving the distance between the plates, doubles C as well.

A capacitor has the property that there is no current flow through it, so that, in the steady state it acts like an open circuit. However, the capacitor can become charged as a result of current flowing towards its positive plate, and discharged as a result of charge flowing away from its positive plate. Therefore, current can flow in a DC circuit containing a capacitor, during the time that the capacitor is charging or discharging.

PARALLEL CAPACITORS
When capacitors are connected in parallel as follows, each branch has the same potential difference or voltage. For two parallel capacitors,

SERIES CAPACITORS
When capacitors are connected in series as follows, the potentials V1 and V2 across the capacitors need not be the same.  Indeed, the total voltage between a and b is V = V1 + V2. If we examine the figure more closely, we note that each capacitor will have the same charge. For two series capacitors,

ENERGY OF CAPACITORS
If a capacitor is charged to a difference of potential V, then the energy stored in a capacitor can be written as

The energy that is stored in a capacitor can be viewed as the energy stored in these electric fields. The entry density within the capacitor may be expressed as,

DIELECTRICS
A dielectric is a medium or substance that transmits electric force without conduction. Normal insulating materials are dielectrics. They consist of atoms and molecules that are composed of positively charged nuclei and negatively charged electrons that are tightly bound together with no loose outer electrons that are free to roam. In the presence of an electric field the positive and negative charges in the atoms and molecules are pulled in opposite directions. As a result, the atoms and molecules will become somewhat “polarized” with the positive and negative charges becoming slightly separated from their equilibrium positions. We will then have tiny “dipoles” throughout the material. [See the beginning sketch above.]

POLARIZE
See DIELECTRICS.

DIPOLES
See DIELECTRICS.

DIELECTRIC CONSTANT
If the polarization is proportional to the field, then the new total field will be proportional to the field that would be produced in the absence of the dielectric material. We can then write that E = E0/κ, where E is the total field in the presence of the dielectric, E0 is the field that would be present without the dielectric and κ is the “dielectric constant” of the material. These dielectric constants vary from material to material.

PERMITTIVITY
Permittivity (ε) is a measure of the electric polarizability of a dielectric. A material with high permittivity polarizes more in response to an applied electric field than a material with low permittivity, thereby storing more energy in the material. In electrostatics, the permittivity plays an important role in determining the capacitance of a capacitor. ε0 is called the permittivity of free space. ε = κε0 is called the “permittivity” of the material.

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Mathematical Results

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April 25, 2023 – 8:46 PM Categories: Physics | Post a comment

Comments on Nietzsche

Reference: Friedrich Nietzsche

June 5, 2011
From Wikipedia: Friedrich Nietzsche

(quotes from Wikipedia are in italics) 

Nietzsche’s works remain controversial, and there is widespread disagreement about their interpretation and significance. Part of the difficulty in interpreting Nietzsche arises from the uniquely provocative style of his philosophical writing. Nietzsche frequently delivered trenchant critiques of Christianity in the most offensive and blasphemous terms possible given the context of 19th century Europe. These aspects of Nietzsche’s style run counter to traditional values in philosophical writing, and they alienated him from the academic establishment both in his time and, to a lesser extent, today.

When looking at knowledge some people react to the writing style.  Usually, one is influenced by the writing style to the degree one is looking through a filter that reacts to that style.  It is possible to look at knowledge without being influenced by the writing style, and simply recognize knowledge for what it is.  Please see Looking at Knowledge.

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A few of the themes that Nietzsche scholars have devoted the most attention to include Nietzsche’s views on morality, his view that “God is dead” (and along with it any sort of God’s-eye view on the world thus leading to perspectivism), his notions of the will to power and Übermensch, and his suggestion of eternal return.

Morality may be defined as a cultural filter deemed necessary for the proper functioning of that culture. It codifies what is right and wrong from the viewpoint of that culture. It is not an absolute code even when presented that way in some cultures. A culture may be improved by improving its sense of morality.

It seems that Nietzsche was trying to do just that. He declared “God is dead” simply to de-emphasize the use of God to present morality as absolute. It was Nietzsche’s way of saying that the conventional Christian God is no longer a viable source of any absolute moral principles.

Nietzsche’s notion of the will to power seems to emphasize that man does not have to be subservient to some arbitrary will of God. His notion of Übermensch seems to emphasize that man can be fully responsible without requiring “God” as a prop.  In my view Nietzsche is right on both counts.

Nietzsche’s suggestion of eternal return is a concept inherent in Hinduism that the universe has been recurring, and will continue to recur, in a self-similar form an infinite number of times across infinite time and/or infinite space. What it really means is that the universe is a perception of “unknowable” through a viewpoint. The universe is there as long as a viewpoint is there.

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June 12, 2011
From Wikipedia: Friedrich Nietzsche on Morality 

Nietzsche rejected the established laws and institutions of his time as they encouraged pretension of virtues, moral or religious beliefs, principles, etc., when one did not really possess them. His motto became, “Be, what you are.” He believed that one should follow one’s own “inner law,” and let morality shape itself. One’s uniquenessness should not be suppressed because of some arbitrary sense of morality.

In Nietzsche’s view, the sense of good and evil impressed by Jewish and Christian traditions was born out of a feeling of inferiority. It was designed to make one not feel inferior, but it did not resolve the individual situation. Nietzsche then tried to present a new, more naturalistic source of value in the vital impulses of life itself.

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April 23, 2023 – 9:24 AM Categories: Philosophy | Post a comment

KHTK Factor # 3

Reference: The KHTK Factors

KHTK Factor # 3: The being is the viewpoint. 

The beingness has the goal to know the Unknowable; and it acquires certain behavior characteristics, which are quite flexible. We may refer to these characteristics as constituting the viewpoint, which shapes the view of beingness. This is the being.

Each being is a specific viewpoint, which is fluid and not fixed. All beings together form a consistent whole per the principle of oneness.

Any fixation is unnatural. A common fixation shows up as the desire for immortality. This desire keeps the being tied to samsara (the phenomenal world).

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Scientology

Compare the above to the following factor in Scientology.

Scientology Factor # 3. The first action of beingness is to assume a viewpoint.

In Scientology, the beingness is called theta, and the being is called thetan. Viewpoint as a point of awareness from which the thetan (not theta) can perceive.

Scientology believes thetan to be eternal like God.

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Logic

The ideal scene of logic is defined by the principle of oneness. Logics starts with the postulates. All postulates are part of a consistent whole per logic. Beingness and all beings are part of that consistent whole.

PRINCIPLE OF ONENESS
Oneness does not imply sameness. Oneness means that all that is known is continuous, consistent and harmonious. This principle of oneness underlies the very concept of the universe. It also underlies the Scientific method. This principle gives us the ideal scene for logic, because its violation gives us anomalies. 

ANOMALY
An anomaly is any violation of the principle of oneness, such as, discontinuity (missing data), inconsistency (contradictory data), or disharmony (arbitrary data).

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April 23, 2023 – 5:12 AM Categories: KHTK | Post a comment

KHTK Factor # 1-1

Reference: The KHTK Factors

KHTK Factor # 1-1: In the beginning and forever is the ability to postulate and become aware.

One knows by able to postulate and become aware of what one has postulated. To postulate is to put something there as truth, which is to be followed up with reasoning.

Thus there is the ability to postulate and to become aware. In the deepest sense, this ability defines each one of us. This is the ’Self’ of the Vedas (written with the upper case ‘S’). This ability is symbolized as SHAKTI, compared to the Unknowable, which is symbolized as SHIVA.

Thus, SHIVA is attempting to know itself through its SHAKTI.

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Scientology

In Scientology, the ability to postulate and to become aware is not stated explicitly. Instead, it is assumed to be part of the general concept of Cause. See KHTK Factor # 1.

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Logic

In the beginning, there is the Unknowable; and the ability to postulate and to be aware per KHTK.

In Scientology, there is only the general concept of Cause.

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April 21, 2023 – 5:04 PM Categories: KHTK | Comments (1)

KHTK Factor # 1

Reference: The KHTK Factors

KHTK Factor # 1: Before the beginning was the Unknowable and the entire purpose of the Unknowable was to know itself.

We do not know about the cause of the universe, nor do we know about the beginning of the universe. What keeps the universe running eternally, is also unknowable. Neither religion nor science has any clue to it.

It is, therefore, natural to start with the postulate of Unknowable. The ancients have symbolized the Unknowable as BRAHMA or SHIVA. The Unknowable has been described beautifully in The Creation Hymn of Rig Veda.

The Unknowable has also been part of the philosophy of Herbert Spencer. See HERBERT SPENCER: The Unknowable.

In Scientology, the Unknowable is described as a “knowable” STATIC, which is very confusing. See The Definition of STATIC.

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Scientology

Compare the above to the following factor in Scientology.

Scientology Factor # 1. Before the beginning was a Cause and the entire purpose of the Cause was the creation of effect.

Scientology defines the Unknowable as Static; but it also assigns Cause as a property to this Static. A causative Static is the postulate with which the philosophy of Scientology begins. Thus, its philosophy identifies everything with either cause or effect.

In Scientology, even the Unknowable is identified with cause making it knowable.

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Logic

Eastern philosophy starts from a point of Unknowingness; whereas, the Western philosophy starts from a point of Knowingness. This is reflected in the God of Abrahamic religions, and in the Know to Mystery Scale of Scientology.

Nobody can make the claim to Total knowingness. No matter how much we know, there is always more to know. Logically, the background of knowingness is unknowingness. It is not the other way around.

Logic begins with postulates.

Wisdom begins when we know that we don’t really know.

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April 20, 2023 – 5:31 AM Categories: KHTK | Comments (1)