# Electrostatic induction

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Electrostatic induction, also known as "electrostatic influence" or simply "influence" in Europe and Latin America, is a redistribution of electric charge in an object, caused by the influence of nearby charges. [1] In the presence of a charged body, an insulated conductor develops a positive charge on one end and a negative charge on the other end. [1] Induction was discovered by British scientist John Canton in 1753 and Swedish professor Johan Carl Wilcke in 1762. [2] Electrostatic generators, such as the Wimshurst machine, the Van de Graaff generator and the electrophorus, use this principle. Due to induction, the electrostatic potential (voltage) is constant at any point throughout a conductor. [3] Electrostatic Induction is also responsible for the attraction of light nonconductive objects, such as balloons, paper or styrofoam scraps, to static electric charges. Electrostatic induction laws apply in dynamic situations as far as the quasistatic approximation is valid. Electrostatic induction should not be confused with Electromagnetic induction.

Electric charge is the physical property of matter that causes it to experience a force when placed in an electromagnetic field. There are two types of electric charge: positive and negative. Like charges repel and unlike attract. An object with an absence of net charge is referred to as neutral. Early knowledge of how charged substances interact is now called classical electrodynamics, and is still accurate for problems that do not require consideration of quantum effects.

John Canton FRS was a British physicist. He was born in Middle Street Stroud, Gloucestershire, the son of a weaver John Canton and Esther. At the age of nineteen, under the auspices of Dr Henry Miles, he was articled for five years as clerk to Samuel Watkins, the master of a school in Spital Square, London, with whom at the end of that time he entered into partnership.

An electrostatic generator, or electrostatic machine, is an electromechanical generator that produces static electricity, or electricity at high voltage and low continuous current. The knowledge of static electricity dates back to the earliest civilizations, but for millennia it remained merely an interesting and mystifying phenomenon, without a theory to explain its behavior and often confused with magnetism. By the end of the 17th century, researchers had developed practical means of generating electricity by friction, but the development of electrostatic machines did not begin in earnest until the 18th century, when they became fundamental instruments in the studies about the new science of electricity. Electrostatic generators operate by using manual power to transform mechanical work into electric energy. Electrostatic generators develop electrostatic charges of opposite signs rendered to two conductors, using only electric forces, and work by using moving plates, drums, or belts to carry electric charge to a high potential electrode. The charge is generated by one of two methods: either the triboelectric effect (friction) or electrostatic induction.

## Explanation

Demonstration of induction, in the 1870s. The positive terminal of an electrostatic machine (right) is placed near an uncharged brass cylinder (left), causing the left end to acquire a positive charge and the right to acquire a negative charge. The small pith ball electroscopes hanging from the bottom show that the charge is concentrated at the ends.
Styrofoam peanuts clinging to a cat's fur. The static electricity that builds up on the fur causes a polarization of the molecules of the styrofoam due to electrostatic induction, resulting in a slight attraction of the styrofoam to the charged fur.

A normal uncharged piece of matter has equal numbers of positive and negative electric charges in each part of it, located close together, so no part of it has a net electric charge. The positive charges are the atoms' nuclei which are bound into the structure of matter and are not free to move. The negative charges are the atoms' electrons. In electrically conductive objects such as metals, some of the electrons are able to move freely about in the object.

An atom is the smallest constituent unit of ordinary matter that constitutes a chemical element. Every solid, liquid, gas, and plasma is composed of neutral or ionized atoms. Atoms are extremely small; typical sizes are around 100 picometers. They are so small that accurately predicting their behavior using classical physics – as if they were billiard balls, for example – is not possible. This is due to quantum effects. Current atomic models now use quantum principles to better explain and predict this behavior.

The electron is a subatomic particle, symbol
e
or
β
, whose electric charge is negative one elementary charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary particles because they have no known components or substructure. The electron has a mass that is approximately 1/1836 that of the proton. Quantum mechanical properties of the electron include an intrinsic angular momentum (spin) of a half-integer value, expressed in units of the reduced Planck constant, ħ. Being fermions, no two electrons can occupy the same quantum state, in accordance with the Pauli exclusion principle. Like all elementary particles, electrons exhibit properties of both particles and waves: they can collide with other particles and can be diffracted like light. The wave properties of electrons are easier to observe with experiments than those of other particles like neutrons and protons because electrons have a lower mass and hence a longer de Broglie wavelength for a given energy.

In physics and electrical engineering, a conductor is an object or type of material that allows the flow of charge in one or more directions. Materials made of metal are common electrical conductors. Electrical current is generated by the flow of negatively charged electrons, positively charged holes, and positive or negative ions in some cases.

When a charged object is brought near an uncharged, electrically conducting object, such as a piece of metal, the force of the nearby charge due to Coulomb's law causes a separation of these internal charges. For example, if a positive charge is brought near the object (see picture of cylindrical electrode near electrostatic machine), the electrons in the metal will be attracted toward it and move to the side of the object facing it. When the electrons move out of an area, they leave an unbalanced positive charge due to the nuclei. This results in a region of negative charge on the object nearest to the external charge, and a region of positive charge on the part away from it. These are called induced charges. If the external charge is negative, the polarity of the charged regions will be reversed.

Coulomb's law, or Coulomb's inverse-square law, is an experimental law of physics that quantifies the amount of force between two stationary, electrically charged particles. The electric force between charged bodies at rest is conventionally called electrostatic force or Coulomb force. The quantity of electrostatic force between stationary charges is always described by Coulomb's law. The law was first published in 1785 by French physicist Charles-Augustin de Coulomb, and was essential to the development of the theory of electromagnetism, maybe even its starting point, because it was now possible to discuss quantity of electric charge in a meaningful way.

Since this process is just a redistribution of the charges that were already in the object, it doesn't change the total charge on the object; it still has no net charge. This induction effect is reversible; if the nearby charge is removed, the attraction between the positive and negative internal charges causes them to intermingle again.

## Charging an object by induction

However, the induction effect can also be used to put a net charge on an object. If, while it is close to the positive charge, the above object is momentarily connected through a conductive path to electrical ground, which is a large reservoir of both positive and negative charges, some of the negative charges in the ground will flow into the object, under the attraction of the nearby positive charge. When the contact with ground is broken, the object is left with a net negative charge.

In electrical engineering, ground or earth is the reference point in an electrical circuit from which voltages are measured, a common return path for electric current, or a direct physical connection to the earth.

This method can be demonstrated using a gold-leaf electroscope, which is an instrument for detecting electric charge. The electroscope is first discharged, and a charged object is then brought close to the instrument's top terminal. Induction causes a separation of the charges inside the electroscope's metal rod, so that the top terminal gains a net charge of opposite polarity to that of the object, while the gold leaves gain a charge of the same polarity. Since both leaves have the same charge, they repel each other and spread apart. The electroscope has not acquired a net charge: the charge within it has merely been redistributed, so if the charged object were to be moved away from the electroscope the leaves will come together again.

An electroscope is an early scientific instrument used to detect the presence of electric charge on a body. It detects charge by the movement of a test object due to the Coulomb electrostatic force on it. The amount of charge on an object is proportional to its voltage. The accumulation of enough charge to detect with an electroscope requires hundreds or thousands of volts, so electroscopes are used with high voltage sources such as static electricity and electrostatic machines. An electroscope can only give a rough indication of the quantity of charge; an instrument that measures electric charge quantitatively is called an electrometer.

But if an electrical contact is now briefly made between the electroscope terminal and ground, for example by touching the terminal with a finger, this causes charge to flow from ground to the terminal, attracted by the charge on the object close to the terminal. This charge neutralizes the charge in the gold leaves, so the leaves come together again. The electroscope now contains a net charge opposite in polarity to that of the charged object. When the electrical contact to earth is broken, e.g. by lifting the finger, the extra charge that has just flowed into the electroscope cannot escape, and the instrument retains a net charge. The charge is held in the top of the electroscope terminal by the attraction of the inducing charge. But when the inducing charge is moved away, the charge is released and spreads throughout the electroscope terminal to the leaves, so the gold leaves move apart again.

The sign of the charge left on the electroscope after grounding is always opposite in sign to the external inducing charge. [4] The two rules of induction are: [4] [5]

• If the object is not grounded, the nearby charge will induce equal and opposite charges in the object.
• If any part of the object is momentarily grounded while the inducing charge is near, a charge opposite in polarity to the inducing charge will be attracted from ground into the object, and it will be left with a charge opposite to the inducing charge.

## The electrostatic field inside a conductive object is zero

A remaining question is how large the induced charges are. The movement of charges is caused by the force exerted on them by the electric field of the external charged object, by Coulomb's law. As the charges in the metal object continue to separate, the resulting positive and negative regions create their own electric field, which opposes the field of the external charge. [3] This process continues until very quickly (within a fraction of a second) an equilibrium is reached in which the induced charges are exactly the right size to cancel the external electric field throughout the interior of the metal object. [3] [6] Then the remaining mobile charges (electrons) in the interior of the metal no longer feel a force and the net motion of the charges stops. [3]

## Induced charge resides on the surface

Since the mobile charges in the interior of a metal object are free to move in any direction, there can never be a static concentration of charge inside the metal; if there was, it would attract opposite polarity charge to neutralize it. [3] Therefore in induction, the mobile charges move under the influence of the external charge until they reach the surface of the metal and collect there, where they are constrained from moving by the boundary. [3]

This establishes the important principle that electrostatic charges on conductive objects reside on the surface of the object. [3] [6] External electric fields induce surface charges on metal objects that exactly cancel the field within. [3]

## The voltage throughout a conductive object is constant

The electrostatic potential or voltage between two points is defined as the energy (work) required to move a small charge through an electric field between the two points, divided by the size of the charge. If there is an electric field directed from point ${\displaystyle \mathbf {b} }$ to point ${\displaystyle \mathbf {a} }$ then it will exert a force on a charge moving from ${\displaystyle \mathbf {a} }$ to ${\displaystyle \mathbf {b} }$. Work will have to be done on the charge by a force to make it move to ${\displaystyle \mathbf {b} }$ against the opposing force of the electric field. Thus the electrostatic potential energy of the charge will increase. So the potential at point ${\displaystyle \mathbf {b} }$ is higher than at point ${\displaystyle \mathbf {a} }$. The electric field ${\displaystyle \mathbf {E} }$ at any point is the gradient (rate of change) of the electrostatic potential ${\displaystyle V}$ :

${\displaystyle \nabla V=\mathbf {E} \,}$

Since there can be no electric field inside a conductive object to exert force on charges ${\displaystyle (\mathbf {E} =0)\,}$, within a conductive object the gradient of the potential is zero [3]

${\displaystyle \nabla V=\mathbf {0} \,}$

Another way of saying this is that in electrostatics, electrostatic induction ensures that the potential (voltage) throughout a conductive object is constant.

## Induction in dielectric objects

A similar induction effect occurs in nonconductive (dielectric) objects, and is responsible for the attraction of small light nonconductive objects, like balloons, scraps of paper or Styrofoam, to static electric charges [7] [8] [9] [10] (see cat, above), as well as static cling in clothes.

In nonconductors, the electrons are bound to atoms or molecules and are not free to move about the object as in conductors; however they can move a little within the molecules. If a positive charge is brought near a nonconductive object, the electrons in each molecule are attracted toward it, and move to the side of the molecule facing the charge, while the positive nuclei are repelled and move slightly to the opposite side of the molecule. Since the negative charges are now closer to the external charge than the positive charges, their attraction is greater than the repulsion of the positive charges, resulting in a small net attraction of the molecule toward the charge. This is called polarization, and the polarized molecules are called dipoles. This effect is microscopic, but since there are so many molecules, it adds up to enough force to move a light object like Styrofoam. This is the principle of operation of a pith-ball electroscope. [11]

## Notes

1. "Electrostatic induction". Encyclopædia Britannica Online. Encyclopædia Britannica, Inc. 2008. Retrieved 2008-06-25.
2. "Electricity". Encyclopædia Britannica, 11th Ed. 9. The Encyclopædia Britannica Co. 1910. p. 181. Retrieved 2008-06-23.
3. Purcell, Edward M.; David J. Morin (2013). Electricity and Magnetism. Cambridge Univ. Press. pp. 127–128. ISBN   1107014026.
4. Cope, Thomas A. Darlington. Physics. Library of Alexandria. ISBN   1465543724.
5. Hadley, Harry Edwin (1899). Magnetism & Electricity for Beginners. Macmillan & Company. p. 182.
6. Saslow, Wayne M. (2002). Electricity, magnetism, and light. US: Academic Press. pp. 159–161. ISBN   0-12-619455-6.
7. Sherwood, Bruce A.; Ruth W. Chabay (2011). Matter and Interactions, 3rd Ed. USA: John Wiley and Sons. pp. 594–596. ISBN   0-470-50347-5.
8. Paul E. Tippens, Electric Charge and Electric Force, Powerpoint presentation, p.27-28, 2009, S. Polytechnic State Univ. Archived April 19, 2012, at the Wayback Machine on DocStoc.com website
9. Henderson, Tom (2011). "Charge and Charge Interactions". Static Electricity, Lesson 1. The Physics Classroom. Retrieved 2012-01-01.
10. Winn, Will (2010). Introduction to Understandable Physics Vol. 3: Electricity, Magnetism and Ligh. USA: Author House. p. 20.4. ISBN   1-4520-1590-2.
11. Kaplan MCAT Physics 2010-2011. USA: Kaplan Publishing. 2009. p. 329. ISBN   1-4277-9875-3. Archived from the original on 2014-01-31.