Charge

In physics, a charge may refer to one of many different quantities, such as the electric charge in electromagnetism or the color charge in quantum chromodynamics. Charges are associated with conserved quantum numbers.

Electric charge

Electric charge is the physical property of matter that causes it to experience a force when close to other electrically charged matter. There are two types of electric charges, called positive and negative. Positively charged substances are repelled from other positively charged substances, but attracted to negatively charged substances; negatively charged substances are repelled from negative and attracted to positive. An object will be negatively charged if it has an excess of electrons, and will otherwise be positively charged or uncharged. The SI unit of electric charge is the coulomb (C), although in electrical engineering it is also common to use the ampere-hour (Ah), and in chemistry it is common to use the elementary charge (e) as a unit. The symbol Q is often used to denote a charge.

The electric charge is a fundamental conserved property of some subatomic particles, which determines their electromagnetic interaction. Electrically charged matter is influenced by, and produces, electromagnetic fields. The interaction between a moving charge and an electromagnetic field is the source of the electromagnetic force, which is one of the four fundamental forces.

Twentieth-century experiments demonstrated that electric charge is quantized; that is, it comes in integer multiples of individual small units called the elementary charge, e, approximately equal to 1.602×10−19 coulombs (except for particles called quarks, which have charges that are integer multiples of e/3). The proton has a charge of e, and the electron has a charge of −e.

Overview

Charge is the fundamental property of forms of matter that exhibit electrostatic attraction or repulsion in the presence of other matter. Electric charge is a characteristic property of many subatomic particles. The charges of free-standing particles are integer multiples of the elementary charge e; we say that electric charge is quantized. Michael Faraday, in his electrolysis experiments, was the first to note the discrete nature of electric charge. Robert Millikan's oil-drop experiment demonstrated this fact directly, and measured the elementary charge.

During the formation of macroscopic objects, usually the constituent atoms and ions will combine in such a manner that they form structures composed of neutral ionic compounds electrically bound to neutral atoms. Thus macroscopic objects tend toward being neutral overall, but macroscopic objects are rarely perfectly net neutral.

There are times when macroscopic objects contain ions distributed throughout the material, rigidly bound in place, giving an overall net positive or negative charge to the object. Also, macroscopic objects made of conductive elements, can more or less easily (depending on the element) take on or give off electrons, and then maintain a net negative or positive charge indefinitely. When the net electric charge of an object is non-zero and motionless, the phenomenon is known as static electricity. Charge can easily be produced by rubbing two dissimilar materials together, such as rubbing amber with fur or glass with silk.

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In this way non-conductive materials can be charged to a significant degree, either positively or negatively.

Finding The Charge on e- using MODE i.e. ________Millikan Oil Drop Experiment

•The Oil-Drop Experiment involved ionizing droplets of oil as they fell through the air, and balancing the force of gravity with the force of an electric applied by electrodes above and below the droplet.

•Millikan could not directly count the number of electrons on each oil droplet, but found that the common denominator between all measured charges was equal to 1.5924 ×10−19 C, and thus concluded that this value was the charge of an electron.

•The measured value of an electron's charge, 1.5924 ×10−19 C, differs from the accepted value of 1.602176487 ×10−19 C by less than one percent.

Voltage:

The amount of electrostatic potential between two points in space.

Electric field:

A region of space around a charged particle, or between two voltages; it exerts a force on charged objects in its vicinity.

Terminal velocity:

The speed at which an object in free-fall and not in a vacuum ceases to accelerate downwards because the force of gravity is equal and opposite of the drag force acting against it.

The Oil-Drop Experiment:

The Oil-Drop Experiment, otherwise known as the Millikan Oil-Drop Experiment, is one of the most influential studies in the history of physical science.

Performed by Robert Millikan and Harvey Fletcher in 1911, the experiment was designed to determine the charge of a single electron, otherwise known as the elementary electric charge. Millikan designed his experiment to measure the force on oil droplets between two electrodes.

He used an atomizer to spray a mist of tiny oil droplets into a chamber, which included a hole. Some droplets would fall through this hole and into a chamber, where he measured their terminal velocity and calculated their mass. Millikan then exposed the droplets to X-rays, which ionized molecules in the air and caused electrons to attach to the oil droplets, thus making them charged. The top and bottom of the chamber were attached to a battery, and the potential difference between the top and bottom produced an electric field that acted on the charged oil drops.

Adjusting the voltage perfectly, Millikan was able to balance the force of gravity (which was exerted downward) with the force of the electric field on the charged particles (which was exerted upward), causing the oil droplets to be suspended in mid-air. A visual representation of the experiment can be seen in the figure:

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Millikan then calculated the charge on particles suspended in mid-air. His assumptions were that the force of gravity, which is the product of mass (m) and gravitational acceleration (g), was equal to the force of the electric field (the product of the charge (q) and the electric field (E)):

Although the charge of each droplet was unknown, Millikan adjusted the strength of the X-rays ionizing the air and measured many values of (q) from many different oil droplets. In each instance, the charge measured was a multiple of 1.5924 ×10−19 C. Thus, it was concluded that the elementary electric charge was 1.5924 ×10−19 C.

The results were very accurate. The calculated value from the Oil-Drop Experiment differs by less than one percent of the current accepted value of 1.602176487 ×10−19 C.

The Oil-Drop Experiment was tremendously influential at the time, not only for determining the charge of an electron, but for helping prove the existence of particles smaller than atoms. At the time, it was not fully accepted that protons, neutrons, and electrons existed.

Conductors and InsulatorsSome substances readily allow passage of electricity through them, others do not. Those which allow electricity to pass through them easily are called conductors. They have electric charges (electrons) that are comparatively free to move inside the material. Metals, human and animal bodies and earth are conductors. Most of the non-metals like glass, porcelain, plastic, nylon, wood offer high resistance to the passage of electricity through them. They are called insulators. Most substances fall into one of the two classes stated above.

When some charge is transferred to a conductor, it readily gets distributed over the entire surface of the conductor. In contrast, if some charge is put on an insulator, it stays at the same place. You will learn why this happens in the next chapter. This property of the materials tells you why a nylon or plastic comb gets electrified on combing dry hair or on rubbing, but a metal article like spoon does not. The charges on metal leak through our body to the ground as both are conductors of electricity. When we bring a charged body in contact with the earth, all the excess charge on the body disappears by causing a momentary current to pass to the ground through the connecting conductor (such as our body). This process of sharing the charges with the earth is called grounding or earthing.

Earthing provides a safety measure for electrical circuits and appliances. A thick metal plate is buried deep into the earth and thick wires are drawn from this plate; these are used in buildings for the purpose of earthing near the mains supply. The electric wiring in our houses has three wires: live, neutral and earth. The first two carry electric current from the power station and the third is earthed by connecting it to the buried metal plate. Metallic bodies of the electric appliances such as electric iron, refrigerator, TV are connected to the earth wire. When any fault occurs or live wire touches the metallic body, the charge flows to the earth without damaging the appliance and without causing any injury to the humans; this would have otherwise been unavoidable since the human body is a conductor of electricity.

Static electricity and electric current Static electricity and electric current are two separate phenomena, both involving electric charge, and may occur simultaneously in the same object. Static electricity is a reference to the electric charge of an

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object and the related electrostatic discharge when two objects are brought together that is not at equilibrium. An electrostatic discharge creates a change in the charge of each of the two objects. In contrast, electric current is the flow of electric charge through an object, which produces no net loss or gain of electric charge.

Electrification by friction

Let a piece of glass and a piece of resin, neither of which exhibiting any electrical properties, be rubbed together and left with the rubbed surfaces in contact. They will still exhibit no electrical properties. Let them be separated. They will now attract each other.

If a second piece of glass be rubbed with a second piece of resin, and if the piece be then separated and suspended in the neighborhood of the former pieces of glass and resin, it may be observed:

1. That the two pieces of glass repel each other.

2. That each piece of glass attracts each piece of resin.

3. That the two pieces of resin repel each other.

These phenomena of attraction and repulsion are called electrical phenomena, and the bodies that exhibit them are said to be 'electrified', or to be 'charged with electricity'.

Bodies may be electrified in many other ways, as well as by friction.

The electrical properties of the two pieces of glass are similar to each other but opposite to those of the two pieces of resin: The glass attracts what the resin repels and repels what the resin attracts.

No force, either of attraction or of repulsion, can be observed between an electrified body and a body nonelectrified.

Actually, all bodies are electrified, but may appear not to be so by the relative similar charge of neighboring objects in the environment. An object further electrified + or - creates an equivalent or opposite charge by default in neighboring objects, until those charges can equalize. The effects of attraction can be observed in high-voltage experiments, while lower voltage effects are merely weaker and therefore less obvious. The attraction and repulsion forces are codified by Coulomb's Law (attraction falls off at the square of the distance, which has a corollary for acceleration in a gravitational field, suggesting that gravitation may be merely electrostatic phenomenon between relatively weak charges in terms of scale).

Electrification by induction

Electrostatic induction is a redistribution of electrical charge in an object, caused by the influence of nearby charges. Induction was discovered by British scientist John Canton in 1753 and Swedish professor Johan Carl Wilcke in 1762. Electrostatic generators, such as the Wimshurst machine, the Van de Graaff generator and the electrophorus, use this principle. Induction is also responsible for the attraction of light nonconductive objects, such as balloons, paper or Styrofoam scraps, to static electric charges.

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.

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When a charged object is brought near an uncharged object, electrically conducting object, such as a piece of metal, the force of the nearby charge causes a separation of these charges. For example, if a positive charge is brought near the object, 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.

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.

Induction 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 redistribution 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 charge were to be moved away from the electroscope the leaves will come together again.

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. 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. So the gold leaves remain separated even after the nearby charged object is moved away.

The sign of the charge left on the electroscope after grounding is always opposite in sign to the external inducing charge. On the other hand, an opposite permanent charge on an object can be achieved if it is grounded from the opposite edge to that which is bearing the external induction charge.

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Basic Properties of Charge

(i) Additivity of charges

•Charges adds up like real numbers i. e., they are Scalars more clearly if any system has n number of charges q1, q2, q3, qn then total charge of the system is

q = q1 + q2 + q3 + ................ qn

•Proper sign have to be used while adding the charges for example if

q1 = +1C

q2 = -2C

q3 = +4C

Then total charge of the system is

q = q1 + q2 + q3

q = (+1) + (-2) + (+4) C

q = (+3) C

(ii) Charge is conserved

•Charge of an isolated system is conserved.

•Charge cannot be created or destroyed but charged particles can be created or destroyed.

(iii) Quantization of charge

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Gold-leaf electroscope, showing induction, before the terminal is grounded.

All free charges are integral multiples of a unit of charge e, where e = -1.602 × 10 -19 C i. e., charge on an electron or proton.

Thus charge q on a body is always denoted by

q = ne

Where n = any integer positive or negative

(iv) Invariance

Like mass, electric charge in a closed system is conserved. As long as a system is impermeable, the amount of charge inside it will neither increase nor decrease; it can only be transferred. However, electric charge differs from other properties—like mass—in that it is a relativistic invariant. That is, charge is independent of speed. The mass of a particle will rise exponentially as its speed approaches that of light, its charge, however, will remain constant.

The independence of electric charge from speed was proven through an experiment in which one fast-moving helium nucleus (two protons and two neutrons bound together) was proven to have the same charge as two separate, slow-moving deuterium nuclei (one proton and one neutron bound together in each nucleus).

From this we get that-

Coulomb’s Law

Coulomb's law is the law of forces between electric charges.

Statement- “It states that two stationary point charges q1 and q2 repel or attract each other with a force F which is directly proportional to the product of charges and inversely proportional to the square of distance between them."

If the two charges have the same sign, the electrostatic force between them is repulsive; if they have different sign, the force between them is attractive. The scalar and vector forms of the mathematical equation are-

&

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mr = m0 / √ (1 - v2/c2)

The Electric Field

Suppose we have a point charge q0 located at r and a set of external charges conspire so as to exert a force F on this charge. We can define the electric field at the point r by:

_____________________________________________________________ (1.1)

The (vector) value of the E field depends only on the values and locations of the external charges, because from Coulomb’s law the force on any “test charge” q0 is proportional to the value of the charge. However to make this definition really kosher we have to stipulate that the test charge q0 is “small”; otherwise its presence will significantly influence the locations of the external charges.

Turning Eq. 1.1 around, we can say that if the electric field at some point r has the value E then a small charge placed at r will experience a force

________________________________________________________________ (1.2)

The electric field is a vector. From Eq. 1.1 we can see that its SI units must be N/C. It follows from Coulomb’s law that the electric field at point r due to a charge q located at the origin is given by

__________________________________________________________ (1.3)

Where ṝ is the unit vector which points in the same direction as r.

Electric Field Lines Due to Charged Particle

From Coulomb’s law we get that-

Since electric field varies as inverse of square of the distance that points from the charge the vector gets shorter as you go away from the origin and they always points radially outwards.

Connecting up these vectors to form a line is a nice way to represent this field.  The magnitude of the field is indicated by the density of the field lines.

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Magnitude is strong near the center where the field lines are close together, and weak farther out, where they are relatively apart.

So, electric field line is an imaginary line drawn in such a way that its direction at any point is same as the direction of field at that point.

An electric field line is, in general a curve drawn in such a way that the tangent to it at each point is the direction of net field at that point.

Field lines of a single position charge points radially outwards while that of a negative charge is radially inwards as shown below in the figure. 

•Field lines around the system of two positive charges give a different picture and describe the mutual repulsion between them.

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Field lines around a system of a positive and negative charge clearly shows the mutual attraction between them as shown below in the figure.

Some important general properties of field lines are:

•Field lines start from positive charge and end on a negative charge.

•Field lines never cross each other if they do so then at the point of intersection there will be two direction of electric field.

•Electric field lines do not pass through a conductor, this shows that electric field inside a conductor is always zero.

•Electric field lines are continuous curves in a charge free region.

Conservation of electric charge:

Electric charges can neither be created nor destroyed. According to the law of conservation of electric charge, the total charge in an isolated system always remains constant. But the charges can be transferred from one part of the system to another, such that the total charge always

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remains conserved. For example, Uranium (92U238) can decay by emitting an alpha particle (2He4 nucleus) and transforming to Thorium (90Th234).                                                                  92U238   90Th 234 + 2He4

  Total charge before decay = +92e, total charge after decay = 90e + 2e. Hence, the total charge is

conserved i.e. it remains constant.

Electric Dipole

An electric dipole is a pair of charges of opposite sign (±q) separated by a distance d which is usually meant to be small compared to the distance from the charges at which we want to find the electric field. The product qd turns out to be important; the vector which points from the −q charge to the +q charge and has magnitude qd is known as the electric dipole moment for the pair, and is denoted p.

Suppose we form an electric dipole by placing a charge +q at (0, 0, d/2) and a charge −q at (0, 0, −d/2). One can show that when z is much larger than d, the electric field for points on the z axis is

__________________________________ (1.4)

Van de Graaff generatorA Van de Graaff generator is an electrostatic generator which uses a moving belt to accumulate very high amounts of electrical charge on a hollow metal globe on the top of the stand. It was invented by American physicist Robert J. Van de Graaff in 1929. The potential difference achieved in modern Van de Graaff generators can reach 5 megavolts. A tabletop version can produce on the order of 100,000 volts and can store enough energy to produce a visible spark.

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A Van de Graaff generator operates by transferring electric charge from a moving belt to a terminal. First invented in 1929, the Van de Graaff generator became a source of high voltage for accelerating subatomic particles to high speeds, making it a useful tool for fundamental physics research.

A simple Van de Graaff-generator consists of a belt of silk, or a similar flexible dielectric material, running over two metal pulleys, one of which is surrounded by a hollow metal sphere. Two electrodes, (2) and (7), in the form of comb-shaped rows of sharp metal points, are positioned respectively near to the bottom of the lower pulley and inside the sphere, over the upper pulley. Comb (2) is connected to the sphere, and comb (7) to the ground. A high DC potential (with respect to earth) is applied to roller (3); a positive potential in this example.

As the belt passes in front of the lower comb, it receives negative charge that escapes from its points due to the influence of the electric field around the lower pulley, which ionizes the air at the points. As the belt touches the upper roller (6), it transfers some electrons, leaving the roller with a negative charge (if it is insulated from the terminal), which added to the negative charge in the belt generates enough electric field to ionize the air at the points of the upper comb. Electrons then leak from the belt to the upper comb and to the terminal, leaving the belt positively charged as it returns down and the terminal negatively charged. The sphere shields the upper roller and comb from the electric field generated by charges that accumulate at the outer surface of it, causing the discharge and change of polarity of the belt at the upper roller to occur practically as if the terminal were grounded. As the belt continues to move, a constant charging current travels via the belt, and the sphere continues to accumulate negative charge until the rate that charge is being lost (through leakage and corona discharges) equals the charging current. The larger the sphere and the farther it is from ground, the higher will be its final potential.

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Schematic view of a classical Van de Graaff-generator.1) hollow metal sphere2) upper electrode3) upper roller (for example an acrylic glass)4) side of the belt with positive charges5) opposite side of the belt with negative charges6) lower roller (metal)7) lower electrode (ground)8) spherical device with negative charges, used to discharge the main sphere

Electric fluxIn electromagnetism, electric flux is the rate of flow of the electric field through a given area. Electric flux is proportional to the number of electric lines going through a virtual surface. In other words the number of electric lines of force passing through the given surface area which is held perpendicular to the direction of electric lines of force is called electric flux. If the electric field is uniform, the electric flux passing through a surface of vector area S is

Where E is the magnitude of the electric field (having units of V/m), S is the area of the surface, and θ is the angle between the electric field lines and the normal (perpendicular) to S. For a non-uniform electric field, the electric flux dΦE through small surface area dS is given by

(The electric field, E, multiplied by the component of area perpendicular to the field). The electric flux over a surface S is therefore given by the surface integral:

Where E is the electric field and dS is a differential area on the closed surface S with an outward facing surface normal defining its direction.

For a closed Gaussian surface, electric flux is given by:

Where-

E is the electric field,

S is any closed surface,

Q is the total electric charge inside the surface S,

ε0 is the electric constant (a universal constant, also called the "permittivity of free space").

This relation is known as Gauss' law for electric field in its integral form and it is one of the four Maxwell's equations.

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Schematic view of a classical Van de Graaff-generator.1) hollow metal sphere2) upper electrode3) upper roller (for example an acrylic glass)4) side of the belt with positive charges5) opposite side of the belt with negative charges6) lower roller (metal)7) lower electrode (ground)8) spherical device with negative charges, used to discharge the main sphere

It is important to note that while the electric flux is not affected by charges that are not within the closed surface, the net electric field, E, in the Gauss' Law equation, can be affected by charges that lie outside the closed surface. While Gauss' Law holds for all situations, it is only useful for "by hand" calculations when high degrees of symmetry exist in the electric field. Examples include spherical and cylindrical symmetry.

Electrical flux has SI units of volt meters (V m), or, equivalently, newton meters squared per coulomb (N m2 C−1). Thus, the SI base units of electric flux are kg·m3·s−3·A−1.

Its dimensional formula is [L3MT–1I–1].

Gauss's lawIn physics, Gauss's law, also known as Gauss's flux theorem, is a law relating the distribution of electric charge to the resulting electric field.

The law was formulated by Carl Friedrich Gauss in 1835, but was not published until 1867. It is one of the four Maxwell's equations which form the basis of classical electrodynamics.

-Qualitative description of the law 

In words, Gauss's law states that:

The net outward normal electric flux through any closed surface is proportional to the total electric charge enclosed within that closed surface.

Gauss's law has a close mathematical similarity with a number of laws in other areas of physics, such as Gauss's law for magnetism and Gauss's law for gravity. In fact, any "inverse-square law" can be formulated in a way similar to Gauss's law: For example, Gauss's law itself is essentially equivalent to the inverse-square Coulomb's law.

-Equation involving E field 

Gauss's law can be stated using either the electric field E or the electric displacement field D. This section shows some of the forms with E; the form with D is below, as are other forms with E.

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Integral form Gauss's law may be expressed as:

Where ΦE is the electric flux through a closed surface S enclosing any volume V, Q is the total charge enclosed within S, and ε0 is the electric constant. The electric flux ΦE is defined as a surface integral of the electric field:

Where E is the electric field, dA is a vector representing an infinitesimal element of area and • represents the dot product of two vectors.

Since the flux is defined as an integral of the electric field, this expression of Gauss's law is called the integral form.

In summary, Gauss’s Law is usually used in either of two ways:

1) Given the field and the surface then enclosed charge can be found.

2) Given the enclosed charge and sufficient symmetry to choose a convenient surface, then the field can be found.

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