Human capital

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Human_capital 

Human capital is a concept used by social scientists to designate personal attributes considered useful in the production process. It encompasses employee knowledge, skills, know-how, good health, and education. Human capital has a substantial impact on individual earnings. Research indicates that human capital investments have high economic returns throughout childhood and young adulthood.

Human Capital simply refers to as the value that is put on to a company by an employee, which can be measured by the employees competenes and skills.

Companies can invest in human capital, for example, through education and training, enabling improved levels of quality and production.

As a result of his conceptualization and modeling work using Human Capital as a key factor, the 2018 Nobel Prize for Economics was jointly awarded to Paul Romer, who founded the modern innovation-driven approach to understanding economic growth.

In the recent literature, the new concept of task-specific human capital was coined in 2004 by Robert Gibbons, an economist at MIT, and Michael Waldman, an economist at Cornell University. The concept emphasizes that in many cases, human capital is accumulated specific to the nature of the task (or, skills required for the task), and the human capital accumulated for the task are valuable to many firms requiring the transferable skills. This concept can be applied to job-assignment, wage dynamics, tournament, promotion dynamics inside firms, etc.

History

Adam Smith included in his definition of capital "the acquired and useful abilities of all the inhabitants or members of the society". The first use of the

Human capital infographic

term "human capital" may be by Irving Fisher. An early discussion with the phrase "human capital" was from Arthur Cecil Pigou:

There is such a thing as investment in human capital as well as investment in material capital. So soon as this is recognised, the distinction between economy in consumption and economy in investment becomes blurred. For, up to a point, consumption is investment in personal productive capacity. This is especially important in connection with children: reducing unduly expenditure on their consumption may greatly lower their efficiency in after-life. Even for adults, after we have descended a certain distance along the scale of wealth, so that we are beyond the region of luxuries and "unnecessary" comforts, a check to personal consumption is also a check to investment.

But the term only found widespread use in economics after its popularization by economists of the Chicago School, in particular Gary Becker, Jacob Mincer, and Theodore Schultz.

The early 20th century Austrian sociologist Rudolf Goldscheid's theory of organic capital and the human economy also served as a precedent for later concepts of human capital.

The use of the term in the modern neoclassical economic literature dates back to Jacob Mincer's article "Investment in Human Capital and Personal Income Distribution" in the Journal of Political Economy in 1958. Then Theodore Schultz also contributed to the development of the subject matter. The best-known application of the idea of "human capital" in economics is that of Mincer and Gary Becker. Becker's book entitled Human Capital, published in 1964, became a standard reference for many years. In this view, human capital is similar to "physical means of production", e.g., factories and machines: one can invest in human capital (via education, training, medical treatment) and one's outputs depend partly on the rate of return on the human capital one owns. Thus, human capital is a means of production, into which additional investment yields additional output. Human capital is substitutable, but not transferable like land, labor, or fixed capital.

Some contemporary growth theories see human capital as an important economic growth factor. Further research shows the relevance of education for the economic welfare of people.

Adam Smith defined four types of fixed capital (which is characterized as that which affords a revenue or profit without circulating or changing masters). The four types were:

1. useful machines, instruments of the trade;
2. buildings as the means of procuring revenue;
3. improvements of land;
4. the acquired and useful abilities of all the inhabitants or members of the society.

Smith defined human capital as follows:

Fourthly, of the acquired and useful abilities of all the inhabitants or members of the society. The acquisition of such talents, by the maintenance of the acquirer during his education, study, or apprenticeship, always costs a real expense, which is a capital fixed and realized, as it were, in his person. Those talents, as they make a part of his fortune, so do they likewise that of the society to which he belongs. The improved dexterity of a workman may be considered in the same light as a machine or instrument of trade which facilitates and abridges labor, and which, though it costs a certain expense, repays that expense with a profit.

Therefore, Smith argued, the productive power of labor are both dependent on the division of labor:

The greatest improvement in the productive powers of labour, and the greater part of the skill, dexterity, and judgement with which it is any where directed, or applied, seem to have been the effects of the division of labour.

There is a complex relationship between the division of labor and human capital.

In the 1990s, the concept of human capital was extended to include natural abilities, physical fitness and healthiness, which are crucial for an individual's success in acquiring knowledge and skills.

Background

Human capital in a broad sense is a collection of activities – all the knowledge, skills, abilities, experience, intelligence, training and competences possessed individually and collectively by individuals in a population. These resources are the total capacity of the people that represents a form of wealth that can be directed to accomplish the goals of the nation or state or a portion thereof. The human capital is further distributed into three kinds; (1) Knowledge Capital (2) Social Capital (3) Emotional Capital.

Many theories explicitly connect investment in human capital development to education, and the role of human capital in economic development, productivity growth, and innovation has frequently been cited as a justification for government subsidies for education and job skills training.

It was assumed in early economic theories, reflecting the context – i.e., the secondary sector of the economy was producing much more than the tertiary sector was able to produce at the time in most countries – to be a fungible resource, homogeneous, and easily interchangeable, and it was referred to simply as workforce or labor, one of three factors of production (the others being land, and assumed-interchangeable assets of money and physical equipment). Just as land became recognized as natural capital and an asset in itself, human factors of production were raised from this simple mechanistic analysis to human capital. In modern technical financial analysis, the term "balanced growth" refers to the goal of equal growth of both aggregate human capabilities and physical assets that produce goods and services.

The assumption that labor or workforces could be easily modelled in aggregate began to be challenged in 1950s when the tertiary sector, which demanded creativity, begun to produce more than the secondary sector was producing at the time in the most developed countries in the world.

Clark's Sector model the for US economy 1850–2009

Accordingly, much more attention was paid to factors that led to success versus failure where human management was concerned. The role of leadership, talent, even celebrity was explored.

Today, most theories attempt to break down human capital into one or more components for analysis Most commonly, Emotional capital is the set of resources (the personal and social emotional competencies) that is inherent to the person, useful for personal, professional and organizational development, and participates to social cohesion and has personal, economic and social returns (Gendron, 2004, 2008). Social capital, the sum of social bonds and relationships, has come to be recognized, along with many synonyms such as goodwill or brand value or social cohesion or social resilience and related concepts like celebrity or fame, as distinct from the talent that an individual (such as an athlete has uniquely) has developed that cannot be passed on to others regardless of effort, and those aspects that can be transferred or taught: instructional capital. Less commonly, some analyses conflate good instructions for health with health itself, or good knowledge management habits or systems with the instructions they compile and manage, or the "intellectual capital" of teams – a reflection of their social and instructional capacities, with some assumptions about their individual uniqueness in the context in which they work. In general these analyses acknowledge that individual trained bodies, teachable ideas or skills, and social influence or persuasion power, are different.

Management accounting is often concerned with questions of how to model human beings as a capital asset. However it is broken down or defined, human capital is vitally important for an organization's success (Crook et al., 2011); human capital increases through education and experience. Human capital is also important for the success of cities and regions: a 2012 study examined how the production of university degrees and R&D activities of educational institutions are related to the human capital of metropolitan areas in which they are located.

In 2010, the OECD (the Organization of Economic Co-operation and Development) encouraged the governments of advanced economies to embrace policies to increase innovation and knowledge in products and services as an economical path to continued prosperity. International policies also often address human capital flight, which is the loss of talented or trained persons from a country that invested in them, to another country which benefits from their arrival without investing in them.

Measurement of human capital

World Economic Forum Global Human Capital Index

Since 2012 the World Economic Forum has annually published its Global Human Capital Report, which includes the Global Human Capital Index (GHCI). In the 2017 edition, 130 countries are ranked from 0 (worst) to 100 (best) according to the quality of their investments in human capital. Norway is at the top, with 77.12.

World Bank Human Capital Index

Main article: Human Capital Index

In October 2018, the World Bank published the Human Capital Index (HCI) as a measurement of economic success. The Index ranks countries according to how much is invested in education and health care for young people. The World Bank's 2019 World Development Report on The Changing Nature of Work showcases the Index and explains its importance given the impact of technology on labor markets and the future of work. One of the central innovations of the World Bank Human Capital Index was the inclusion and harmonization of learning data across 164 countries. This introduced a measure of human capital which directly accounts for the knowledge and skills acquired from schooling, rather than using schooling alone, now widely recognized to be an incomplete proxy. The learning outcomes data, methodology, and applications to the human capital literature underlying this effort were published in Nature. 

Human Capital Index ranking (top 50 countries):

1.  Singapore 0.88
2.  South Korea 0.84
3.  Japan 0.84
4.  Hong Kong, SAR of China 0.82
5.  Finland 0.81
6.  Ireland 0.81
7.  Australia 0.80
8.  Sweden 0.80
9.  Netherlands 0.80
10.  Canada 0.80
11.  Germany 0.79
12.  Austria 0.79
13.  Slovenia 0.79
14.  Czech Republic 0.78
15.  United Kingdom 0.78
16.  Portugal 0.78
17.  Denmark 0.77
18.  Norway 0.77
19.  Italy 0.77
20.  Switzerland 0.77
21.  New Zealand 0.77
22.  France 0.76
23.  Israel 0.76
24.  United States 0.76
25.  Macau, SAR of China 0.76
26.  Belgium 0.76
27.  Serbia 0.76
28.  Cyprus 0.75
29.  Estonia 0.75
30.  Poland 0.75
31.  Kazakhstan 0.75
32.  Spain 0.74
33.  Iceland 0.74
34.  Russia 0.73
35.  Latvia 0.72
36.  Croatia 0.72
37.  Lithuania 0.71
38.  Hungary 0.70
39.  Malta 0.70
40.  Slovakia 0.69
41.  Luxembourg 0.69
42.  Greece 0.68
43.  Seychelles 0.68
44.  Bulgaria 0.68
45.  Chile 0.67
46.  China 0.67
47.  Bahrain 0.67
48.  Vietnam 0.67
49.  United Arab Emirates 0.66
50.  Ukraine 0.65

Other methods

A new measure of expected human capital calculated for 195 countries from 1990 to 2016 and defined for each birth cohort as the expected years lived from age 20 to 64 years and adjusted for educational attainment, learning or education quality, and functional health status was published by The Lancet in September 2018. Finland had the highest level of expected human capital: 28·4 health, education, and learning-adjusted expected years lived between age 20 and 64 years. Niger had the lowest at less than 1·6 years.

Measuring the human capital index of individual firms is also possible: a survey is made on issues like training or compensation, and a value between 0 (worst) and 100 (best) is obtained. Enterprises which rank high are shown to add value to shareholders.

Human capital management

Main article: Human resource management

Human capital management (HCM) is the term used to describe workforce practices and resources that focus on maximizing needed skills through the recruitment, training, and development of employees. Departments and software applications responsible for HCM often manage tasks that include administrative support, reporting and analytics, education and training, and hiring and recruitment.

Cumulative growth

Human capital is distinctly different from the tangible monetary capital due to the extraordinary characteristic of human capital to grow cumulatively over a long period of time. The growth of tangible monetary capital is not always linear due to the shocks of business cycles. During the period of prosperity, monetary capital grows at relatively higher rate while during the period of recession and depression, there is deceleration of monetary capital. On the other hand, human capital has uniformly rising rate of growth over a long period of time because the foundation of this human capital is laid down by the educational and health inputs. The current generation is qualitatively developed by the effective inputs of education and health. The future generation is more benefited by the advanced research in the field of education and health, undertaken by the current generation. Therefore, the educational and health inputs create more productive impacts upon the future generation and the future generation becomes superior to the current generation. In other words, the productive capacity of future generation increases more than that of current generation. Therefore, rate of human capital formation in the future generation happens to be more than the rate of human capital formation in the current generation. This is the cumulative growth of human capital formation generated by superior quality of manpower in the succeeding generation as compared to the preceding generation.

Intangibility and portability

Human capital is an intangible asset, and it is not owned by the firm that employs it and is generally not fungible. Specifically, individuals arrive at 9am and leave at 5pm (in the conventional office model) taking most of their knowledge and relationships with them.

Human capital when viewed from a time perspective consumes time in one of these key activities:

1. Knowledge (activities involving one employee),
2. Collaboration (activities involving more than 1 employee),
3. Processes (activities specifically focused on the knowledge and collaborative activities generated by organizational structure – such as silo impacts, internal politics, etc.) and
4. Absence (annual leave, sick leave, holidays, etc.).

Despite the lack of formal ownership, firms can and do gain from high levels of training, in part because it creates a corporate culture or vocabulary teams use to create cohesion.

In recent economic writings the concept of firm-specific human capital, which includes those social relationships, individual instincts, and instructional details that are of value within one firm (but not in general), appears by way of explaining some labour mobility issues and such phenomena as golden handcuffs. Workers can be more valuable where they are simply for having acquired this knowledge, these skills and these instincts. Accordingly, the firm gains for their unwillingness to leave and market talents elsewhere.

Marxist analysis

An advertisement for labour from Sabah and Sarawak, seen in Jalan Petaling, Kuala Lumpur.

In some way, the idea of "human capital" is similar to Karl Marx's concept of labor power: he thought in capitalism workers sold their labor power in order to receive income (wages and salaries). But long before Mincer or Becker wrote, Marx pointed to "two disagreeably frustrating facts" with theories that equate wages or salaries with the interest on human capital.

1. The worker must actually work, exert their mind and body, to earn this "interest." Marx strongly distinguished between one's capacity to work, labor power, and the activity of working.
2. A free worker cannot sell his human capital in one go; it is far from being a liquid asset, even more illiquid than shares and land. He does not sell his skills, but contracts to utilize those skills, in the same way that an industrialist sells his produce, not his machinery. The exception here are slaves, whose human capital can be sold, though the slave does not earn an income himself.

An employer must be receiving a profit from his operations, so that workers must be producing what Marx (under the labor theory of value) perceived as surplus-value, i.e., doing work beyond that necessary to maintain their labor power. Though having "human capital" gives workers some benefits, they are still dependent on the owners of non-human wealth for their livelihood.

The term appears in Marx's article in the New-York Daily Tribune "The Emancipation Question," January 17 and 22, 1859, although there the term is used to describe humans who act like a capital to the producers, rather than in the modern sense of "knowledge capital" endowed to or acquired by humans.

Neo-Marxist economists have argued that education leads to higher wages not by increasing human capital, but rather by making workers more compliant and reliable in a corporate environment. The reasoning of which being that higher education creates the illusion of a meritocracy, thus justifying economic inequality to the benefit of capitalists, regardless of whether the educated human capital actually provides additional labor value.

Risk

When human capital is assessed by activity based costing via time allocations it becomes possible to assess human capital risk. Human capital risks can be identified if HR processes in organizations are studied in detail. Human capital risk occurs when the organization operates below attainable operational excellence levels. For example, if a firm could reasonably reduce errors and rework (the Process component of human capital) from 10,000 hours per annum to 2,000 hours with attainable technology, the difference of 8,000 hours is human capital risk. When wage costs are applied to this difference (the 8,000 hours) it becomes possible to financially value human capital risk within an organizational perspective.

Risk accumulates in four primary categories:

1. Absence activities (activities related to employees not showing up for work such as sick leave, industrial action, etc.). Unavoidable absence is referred to as Statutory Absence. All other categories of absence are termed "Controllable Absence";
2. Collaborative activities are related to the expenditure of time between more than one employee within an organizational context. Examples include: meetings, phone calls, instructor led training, etc.;
3. Knowledge Activities are related to time expenditures by a single person and include finding/retrieving information, research, email, messaging, blogging, information analysis, etc.; and
4. Process activities are knowledge and collaborative activities that result due to organizational context such as errors/rework, manual data transformation, stress, politics, etc.

Corporate finance

In corporate finance, human capital is one of the three primary components of intellectual capital (which, in addition to tangible assets, comprise the entire value of a company). Human capital is the value that the employees of a business provide through the application of skills, know-how and expertise. It is an organization's combined human capability for solving business problems. Human capital is inherent in people and cannot be owned by an organization. Therefore, human capital leaves an organization when people leave. Human capital also encompasses how effectively an organization uses its people resources as measured by creativity and innovation. A company's reputation as an employer affects the human capital it draws.

Criticism

Some labor economists have criticized the Chicago-school theory, claiming that it tries to explain all differences in wages and salaries in terms of human capital. One of the leading alternatives, advanced by Michael Spence and Joseph Stiglitz, is "signaling theory". According to signaling theory, education does not lead to increased human capital, but rather acts as a mechanism by which workers with superior innate abilities can signal those abilities to prospective employers and so gain above average wages.

The concept of human capital can be infinitely elastic, including unmeasurable variables such as personal character or connections with insiders (via family or fraternity). This theory has had a significant share of study in the field proving that wages can be higher for employees on aspects other than human capital. Some variables that have been identified in the literature of the past few decades include, gender and nativity wage differentials, discrimination in the work place, and socioeconomic status.

The prestige of a credential may be as important as the knowledge gained in determining the value of an education. This points to the existence of market imperfections such as non-competing groups and labor-market segmentation. In segmented labor markets, the "return on human capital" differs between comparably skilled labor-market groups or segments. An example of this is discrimination against minority or female employees.

Following Becker, the human capital literature often distinguishes between "specific" and "general" human capital. Specific human capital refers to skills or knowledge that is useful only to a single employer or industry, whereas general human capital (such as literacy) is useful to all employers. Economists view firm-specific human capital as risky, since firm closure or industry decline leads to skills that cannot be transferred (the evidence on the quantitative importance of firm specific capital is unresolved).

Human capital is central to debates about welfare, education, health care, and retirement.

In 2004, "human capital" (German: Humankapital) was named the German Un-Word of the Year by a jury of linguistic scholars, who considered the term inappropriate and inhumane, as individuals would be degraded and their abilities classified according to economically relevant quantities.

"Human capital" is often confused with human development. The UN suggests "Human development denotes both the process of widening people's choices and improving their well-being". The UN Human Development indices suggest that human capital is merely a means to the end of human development: "Theories of human capital formation and human resource development view human beings as means to increased income and wealth rather than as ends. These theories are concerned with human beings as inputs to increasing production".

Permittivity

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Permittivity 

 

A dielectric medium showing orientation of charged particles creating polarization effects. Such a medium can have a lower ratio of electric flux to charge (more permittivity) than empty space

In electromagnetism, the absolute permittivity, often simply called permittivity and denoted by the Greek letter ε (epsilon), 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.

In the simplest case, the electric displacement field D resulting from an applied electric field E is

${\displaystyle \mathbf{D}=\epsilon \mathbf{E}.}$

More generally, the permittivity is a thermodynamic function of state. It can depend on the frequency, magnitude, and direction of the applied field. The SI unit for permittivity is farad per meter (F/m).

The permittivity is often represented by the relative permittivity ε_r which is the ratio of the absolute permittivity ε and the vacuum permittivity ε₀

${\displaystyle \kappa ={\epsilon }_{\mathrm{r}}=\frac{\epsilon }{{\epsilon }_0}}$.

This dimensionless quantity is also often and ambiguously referred to as the permittivity. Another common term encountered for both absolute and relative permittivity is the dielectric constant which has been deprecated in physics and engineering as well as in chemistry.

By definition, a perfect vacuum has a relative permittivity of exactly 1 whereas at standard temperature and pressure, air has a relative permittivity of κ_air ≈ 1.0006.

Relative permittivity is directly related to electric susceptibility (χ) by

${\displaystyle \chi =\kappa -1}$

otherwise written as

${\displaystyle \epsilon ={\epsilon }_{\mathrm{r}}{\epsilon }_0=(1+\chi ){\epsilon }_0}$

The term "permittivity" was introduced in the 1880s by Oliver Heaviside to complement Thomson's (1872) "permeability". Formerly written as p, the designation with ε has been in common use since the 1950s.

Units

The standard SI unit for permittivity is farad per meter (F/m or F·m⁻¹).

${\displaystyle \frac{\text{F}}{\text{m}}=\frac{\text{C}}{\text{V}\cdot \text{m}}=\frac{{\text{C}}^2}{\text{N}\cdot {\text{m}}^2}=\frac{{\text{C}}^2\cdot {\text{s}}^2}{\text{kg}\cdot {\text{m}}^3}}$

Explanation

In electromagnetism, the electric displacement field D represents the distribution of electric charges in a given medium resulting from the presence of an electric field E. This distribution includes charge migration and electric dipole reorientation. Its relation to permittivity in the very simple case of linear, homogeneous, isotropic materials with "instantaneous" response to changes in electric field is:

${\displaystyle \mathbf{D}=\epsilon \mathbf{E}}$

where the permittivity ε is a scalar. If the medium is anisotropic, the permittivity is a second rank tensor.

In general, permittivity is not a constant, as it can vary with the position in the medium, the frequency of the field applied, humidity, temperature, and other parameters. In a nonlinear medium, the permittivity can depend on the strength of the electric field. Permittivity as a function of frequency can take on real or complex values.

In SI units, permittivity is measured in farads per meter (F/m or A²·s⁴·kg⁻¹·m⁻³). The displacement field D is measured in units of coulombs per square meter (C/m²), while the electric field E is measured in volts per meter (V/m). D and E describe the interaction between charged objects. D is related to the charge densities associated with this interaction, while E is related to the forces and potential differences.

Vacuum permittivity

Main article: Vacuum permittivity

The vacuum permittivity ε₀ (also called permittivity of free space or the electric constant) is the ratio D/E in free space. It also appears in the Coulomb force constant,

${\displaystyle k_{\text{e}}=\frac{1}{4\pi {\epsilon }_0}}$

Its value is

${\displaystyle {\epsilon }_0\stackrel{\mathrm{d}\mathrm{e}\mathrm{f}}{=}\frac{1}{c_0^2{\mu }_0}\approx 8.8541878128(13)\times {10}^{-12}\text{ F/m }}$

where

• c₀ is the speed of light in free space,
• µ₀ is the vacuum permeability.

The constants c₀ and μ₀ were both defined in SI units to have exact numerical values until the 2019 redefinition of the SI base units. Therefore, until that date, ε₀ could be also stated exactly as a fraction, ${\displaystyle \frac{1}{c_0^2{\mu }_0}=\frac{1}{35950207149.4727056\pi }\text{ F/m}}$ even if the result was irrational (because the fraction contained π). In contrast, the ampere was a measured quantity before 2019, but since then the ampere is now exactly defined and it is μ₀ that is an experimentally measured quantity (with consequent uncertainty) and therefore so is the new 2019 definition of ε₀ (c₀ remains exactly defined before and since 2019).

Relative permittivity

Main article: Relative permittivity

The linear permittivity of a homogeneous material is usually given relative to that of free space, as a relative permittivity ε_r (also called dielectric constant, although this term is deprecated and sometimes only refers to the static, zero-frequency relative permittivity). In an anisotropic material, the relative permittivity may be a tensor, causing birefringence. The actual permittivity is then calculated by multiplying the relative permittivity by ε₀:

${\displaystyle \epsilon ={\epsilon }_{\mathrm{r}}{\epsilon }_0=(1+\chi ){\epsilon }_0,}$

where χ (frequently written χ_e) is the electric susceptibility of the material.

The susceptibility is defined as the constant of proportionality (which may be a tensor) relating an electric field E to the induced dielectric polarization density P such that

${\displaystyle \mathbf{P}={\epsilon }_0\chi \mathbf{E},}$

where ε₀ is the electric permittivity of free space.

The susceptibility of a medium is related to its relative permittivity ε_r by

${\displaystyle \chi ={\epsilon }_{\mathrm{r}}-1.}$

So in the case of a vacuum,

${\displaystyle \chi =0.}$

The susceptibility is also related to the polarizability of individual particles in the medium by the Clausius-Mossotti relation.

The electric displacement D is related to the polarization density P by

${\displaystyle \mathbf{D}={\epsilon }_0\mathbf{E}+\mathbf{P}={\epsilon }_0(1+\chi )\mathbf{E}={\epsilon }_{\mathrm{r}}{\epsilon }_0\mathbf{E}.}$

The permittivity ε and permeability µ of a medium together determine the phase velocity v = c/n of electromagnetic radiation through that medium:

${\displaystyle \epsilon \mu =\frac{1}{v^2}.}$

Practical applications

Determining capacitance

The capacitance of a capacitor is based on its design and architecture, meaning it will not change with charging and discharging. The formula for capacitance in a parallel plate capacitor is written as

${\displaystyle C=\epsilon \frac{A}{d}}$

where ${\displaystyle A}$ is the area of one plate, ${\displaystyle d}$ is the distance between the plates, and ${\displaystyle \epsilon }$ is the permittivity of the medium between the two plates. For a capacitor with relative permittivity ${\displaystyle \kappa }$, it can be said that

${\displaystyle C=\kappa {\epsilon }_0\frac{A}{d}}$

Gauss's law

Permittivity is connected to electric flux (and by extension electric field) through Gauss's law. Gauss's law states that for a closed Gaussian surface, S

${\displaystyle {\mathrm{\Phi }}_E=\frac{Q_{\text{enc}}}{{\epsilon }_0}={\oint }_S\mathbf{E}\cdot \mathrm{d}\mathbf{A}}$

where ${\displaystyle {\mathrm{\Phi }}_E}$ is the net electric flux passing through the surface, ${\displaystyle Q_{\text{enc}}}$ is the charge enclosed in the Gaussian surface, ${\displaystyle \mathbf{E}}$ is the electric field vector at a given point on the surface, and ${\displaystyle \mathrm{d}\mathbf{A}}$ is a differential area vector on the Gaussian surface.

If the Gaussian surface uniformly encloses an insulated, symmetrical charge arrangement, the formula can be simplified to

${\displaystyle EA\cos (\theta )=\frac{Q_{\text{enc}}}{{\epsilon }_0}}$

where ${\displaystyle \theta }$ represents the angle between the electric field lines and the normal (perpendicular) to S.

If all of the electric field lines cross the surface at 90°, the formula can be further simplified to

${\displaystyle E=\frac{Q_{\text{enc}}}{{\epsilon }_{0}A}}$

Because the surface area of a sphere is ${\displaystyle 4\pi r^2}$, the electric field a distance ${\displaystyle r}$ away from a uniform, spherical charge arrangement is

${\displaystyle E=\frac{Q}{{\epsilon }_{0}A}=\frac{Q}{{\epsilon }_0\left(4\pi r^2\right)}=\frac{Q}{4\pi {\epsilon }_0{r}^2}=\frac{kQ}{r^2}}$

where ${\displaystyle k}$ is the Coulomb constant (${\displaystyle \sim 9.0\times {10}^9\text{m}/\text{F}}$). This formula applies to the electric field due to a point charge, outside of a conducting sphere or shell, outside of a uniformly charged insulating sphere, or between the plates of a spherical capacitor.

Dispersion and causality

In general, a material cannot polarize instantaneously in response to an applied field, and so the more general formulation as a function of time is

${\displaystyle \mathbf{P}(t)={\epsilon }_0{\int }_{-\mathrm{\infty }}^t\chi \left(t-t^{\prime }\right)\mathbf{E}\left(t^{\prime }\right)d{t}^{\prime }.}$

That is, the polarization is a convolution of the electric field at previous times with time-dependent susceptibility given by χ(Δt). The upper limit of this integral can be extended to infinity as well if one defines χ(Δt) = 0 for Δt < 0. An instantaneous response would correspond to a Dirac delta function susceptibility χ(Δt) = χδ(Δt).

It is convenient to take the Fourier transform with respect to time and write this relationship as a function of frequency. Because of the convolution theorem, the integral becomes a simple product,

${\displaystyle \mathbf{P}(\omega )={\epsilon }_0\chi (\omega )\mathbf{E}(\omega ).}$

This frequency dependence of the susceptibility leads to frequency dependence of the permittivity. The shape of the susceptibility with respect to frequency characterizes the dispersion properties of the material.

Moreover, the fact that the polarization can only depend on the electric field at previous times (i.e. effectively χ(Δt) = 0 for Δt < 0), a consequence of causality, imposes Kramers–Kronig constraints on the susceptibility χ(0).

Complex permittivity

A dielectric permittivity spectrum over a wide range of frequencies. ε′ and ε″ denote the real and the imaginary part of the permittivity, respectively. Various processes are labeled on the image: ionic and dipolar relaxation, and atomic and electronic resonances at higher energies.

As opposed to the response of a vacuum, the response of normal materials to external fields generally depends on the frequency of the field. This frequency dependence reflects the fact that a material's polarization does not change instantaneously when an electric field is applied. The response must always be causal (arising after the applied field), which can be represented by a phase difference. For this reason, permittivity is often treated as a complex function of the (angular) frequency ω of the applied field:

${\displaystyle \epsilon \to \hat{\epsilon }(\omega )}$

(since complex numbers allow specification of magnitude and phase). The definition of permittivity therefore becomes

${\displaystyle D_0{e}^{-i\omega t}=\hat{\epsilon }(\omega )E_0{e}^{-i\omega t},}$

where

• D₀ and E₀ are the amplitudes of the displacement and electric fields, respectively,
• i is the imaginary unit, i² = −1.

The response of a medium to static electric fields is described by the low-frequency limit of permittivity, also called the static permittivity ε_s (also ε_DC):

${\displaystyle {\epsilon }_{\mathrm{s}}=\underset{\omega \to 0}{lim}\hat{\epsilon }(\omega ).}$

At the high-frequency limit (meaning optical frequencies), the complex permittivity is commonly referred to as ε_∞ (or sometimes ε_opt). At the plasma frequency and below, dielectrics behave as ideal metals, with electron gas behavior. The static permittivity is a good approximation for alternating fields of low frequencies, and as the frequency increases a measurable phase difference δ emerges between D and E. The frequency at which the phase shift becomes noticeable depends on temperature and the details of the medium. For moderate field strength (E₀), D and E remain proportional, and

${\displaystyle \hat{\epsilon }=\frac{D_0}{E_0}=|\epsilon |e^{-i\delta }.}$

Since the response of materials to alternating fields is characterized by a complex permittivity, it is natural to separate its real and imaginary parts, which is done by convention in the following way:

${\displaystyle \hat{\epsilon }(\omega )={\epsilon }^{\prime }(\omega )-i{\epsilon }^{″}(\omega )=\left|\frac{D_0}{E_0}\right|\left(\cos \delta -i\sin \delta \right).}$

where

• ε′ is the real part of the permittivity;
• ε″ is the imaginary part of the permittivity;
• δ is the loss angle.

The choice of sign for time-dependence, e^−iωt, dictates the sign convention for the imaginary part of permittivity. The signs used here correspond to those commonly used in physics, whereas for the engineering convention one should reverse all imaginary quantities.

The complex permittivity is usually a complicated function of frequency ω, since it is a superimposed description of dispersion phenomena occurring at multiple frequencies. The dielectric function ε(ω) must have poles only for frequencies with positive imaginary parts, and therefore satisfies the Kramers–Kronig relations. However, in the narrow frequency ranges that are often studied in practice, the permittivity can be approximated as frequency-independent or by model functions.

At a given frequency, the imaginary part, ε″, leads to absorption loss if it is positive (in the above sign convention) and gain if it is negative. More generally, the imaginary parts of the eigenvalues of the anisotropic dielectric tensor should be considered.

In the case of solids, the complex dielectric function is intimately connected to band structure. The primary quantity that characterizes the electronic structure of any crystalline material is the probability of photon absorption, which is directly related to the imaginary part of the optical dielectric function ε(ω). The optical dielectric function is given by the fundamental expression:

${\displaystyle \epsilon (\omega )=1+\frac{8{\pi }^2{e}^2}{m^2}\sum _{c,v}\int W_{c,v}(E)(\phi (\hslash \omega -E)-\phi (\hslash \omega +E))dx.}$

In this expression, W_c,v(E) represents the product of the Brillouin zone-averaged transition probability at the energy E with the joint density of states, J_c,v(E); φ is a broadening function, representing the role of scattering in smearing out the energy levels. In general, the broadening is intermediate between Lorentzian and Gaussian; for an alloy it is somewhat closer to Gaussian because of strong scattering from statistical fluctuations in the local composition on a nanometer scale.

Tensorial permittivity

According to the Drude model of magnetized plasma, a more general expression which takes into account the interaction of the carriers with an alternating electric field at millimeter and microwave frequencies in an axially magnetized semiconductor requires the expression of the permittivity as a non-diagonal tensor. (see also Electro-gyration).

${\displaystyle \mathbf{D}(\omega )=\left|\begin{array}{ccc}{\epsilon }_1& -i{\epsilon }_2& 0\\ i{\epsilon }_2& {\epsilon }_1& 0\\ 0& 0& {\epsilon }_z\end{array}\right|\mathbf{E}(\omega )}$

If ε₂ vanishes, then the tensor is diagonal but not proportional to the identity and the medium is said to be a uniaxial medium, which has similar properties to a uniaxial crystal.

Classification of materials

Classification of materials based on permittivity

εr″/εr′	Current conduction	Field propagation
0		perfect dielectric lossless medium
≪ 1	low-conductivity material poor conductor	low-loss medium good dielectric
≈ 1	lossy conducting material	lossy propagation medium
≫ 1	high-conductivity material good conductor	high-loss medium poor dielectric
∞	perfect conductor

Materials can be classified according to their complex-valued permittivity ε, upon comparison of its real ε′ and imaginary ε″ components (or, equivalently, conductivity, σ, when accounted for in the latter). A perfect conductor has infinite conductivity, σ = ∞, while a perfect dielectric is a material that has no conductivity at all, σ = 0; this latter case, of real-valued permittivity (or complex-valued permittivity with zero imaginary component) is also associated with the name lossless media. Generally, when σ/ωε′ ≪ 1 we consider the material to be a low-loss dielectric (although not exactly lossless), whereas σ/ωε′ ≫ 1 is associated with a good conductor; such materials with non-negligible conductivity yield a large amount of loss that inhibits the propagation of electromagnetic waves, thus are also said to be lossy media. Those materials that do not fall under either limit are considered to be general media.

Lossy medium

In the case of a lossy medium, i.e. when the conduction current is not negligible, the total current density flowing is:

${\displaystyle J_{\text{tot}}=J_{\mathrm{c}}+J_{\mathrm{d}}=\sigma E+i\omega {\epsilon }^{\prime }E=i\omega \hat{\epsilon }E}$

where

• σ is the conductivity of the medium;
• ${\displaystyle {\epsilon }^{\prime }={\epsilon }_0{\epsilon }_r}$ is the real part of the permittivity.
• ${\displaystyle \hat{\epsilon }={\epsilon }^{\prime }-i{\epsilon }^{″}}$is the complex permittivity

Note that this is using the electrical engineering convention of the Complex conjugate ambiguity; the physics/chemistry convention involves the complex conjugate of these equations.

The size of the displacement current is dependent on the frequency ω of the applied field E; there is no displacement current in a constant field.

In this formalism, the complex permittivity is defined as:

${\displaystyle \hat{\epsilon }={\epsilon }^{\prime }\left(1-i\frac{\sigma }{\omega {\epsilon }^{\prime }}\right)={\epsilon }^{\prime }-i\frac{\sigma }{\omega }}$

In general, the absorption of electromagnetic energy by dielectrics is covered by a few different mechanisms that influence the shape of the permittivity as a function of frequency:

• First are the relaxation effects associated with permanent and induced molecular dipoles. At low frequencies the field changes slowly enough to allow dipoles to reach equilibrium before the field has measurably changed. For frequencies at which dipole orientations cannot follow the applied field because of the viscosity of the medium, absorption of the field's energy leads to energy dissipation. The mechanism of dipoles relaxing is called dielectric relaxation and for ideal dipoles is described by classic Debye relaxation.
• Second are the resonance effects, which arise from the rotations or vibrations of atoms, ions, or electrons. These processes are observed in the neighborhood of their characteristic absorption frequencies.

The above effects often combine to cause non-linear effects within capacitors. For example, dielectric absorption refers to the inability of a capacitor that has been charged for a long time to completely discharge when briefly discharged. Although an ideal capacitor would remain at zero volts after being discharged, real capacitors will develop a small voltage, a phenomenon that is also called soakage or battery action. For some dielectrics, such as many polymer films, the resulting voltage may be less than 1–2% of the original voltage. However, it can be as much as 15–25% in the case of electrolytic capacitors or supercapacitors.

Quantum-mechanical interpretation

In terms of quantum mechanics, permittivity is explained by atomic and molecular interactions.

At low frequencies, molecules in polar dielectrics are polarized by an applied electric field, which induces periodic rotations. For example, at the microwave frequency, the microwave field causes the periodic rotation of water molecules, sufficient to break hydrogen bonds. The field does work against the bonds and the energy is absorbed by the material as heat. This is why microwave ovens work very well for materials containing water. There are two maxima of the imaginary component (the absorptive index) of water, one at the microwave frequency, and the other at far ultraviolet (UV) frequency. Both of these resonances are at higher frequencies than the operating frequency of microwave ovens.

At moderate frequencies, the energy is too high to cause rotation, yet too low to affect electrons directly, and is absorbed in the form of resonant molecular vibrations. In water, this is where the absorptive index starts to drop sharply, and the minimum of the imaginary permittivity is at the frequency of blue light (optical regime).

At high frequencies (such as UV and above), molecules cannot relax, and the energy is purely absorbed by atoms, exciting electron energy levels. Thus, these frequencies are classified as ionizing radiation.

While carrying out a complete ab initio (that is, first-principles) modelling is now computationally possible, it has not been widely applied yet. Thus, a phenomenological model is accepted as being an adequate method of capturing experimental behaviors. The Debye model and the Lorentz model use a first-order and second-order (respectively) lumped system parameter linear representation (such as an RC and an LRC resonant circuit).

Measurement

Main article: Dielectric spectroscopy

The relative permittivity of a material can be found by a variety of static electrical measurements. The complex permittivity is evaluated over a wide range of frequencies by using different variants of dielectric spectroscopy, covering nearly 21 orders of magnitude from 10⁻⁶ to 10¹⁵ hertz. Also, by using cryostats and ovens, the dielectric properties of a medium can be characterized over an array of temperatures. In order to study systems for such diverse excitation fields, a number of measurement setups are used, each adequate for a special frequency range.

Various microwave measurement techniques are outlined in Chen et al.. Typical errors for the Hakki-Coleman method employing a puck of material between conducting planes are about 0.3%.

• Low-frequency time domain measurements (10⁻⁶ to 10³ Hz)
• Low-frequency frequency domain measurements (10⁻⁵ to 10⁶ Hz)
• Reflective coaxial methods (10⁶ to 10¹⁰ Hz)
• Transmission coaxial method (10⁸ to 10¹¹ Hz)
• Quasi-optical methods (10⁹ to 10¹⁰ Hz)
• Terahertz time-domain spectroscopy (10¹¹ to 10¹³ Hz)
• Fourier-transform methods (10¹¹ to 10¹⁵ Hz)

At infrared and optical frequencies, a common technique is ellipsometry. Dual polarisation interferometry is also used to measure the complex refractive index for very thin films at optical frequencies.

For the 3D measurement of dielectric tensors at optical frequency, Dielectric tensor tomography can be used.