University Physics

Chapter 17 Electric Charge and Electric Field

When you scuff your shoes across a carpet, you can get zapped by an annoying spark of static electricity. That same spark could totally destroy the function of a computer chip. Lightning, the same phenomenon on a vast scale, can destroy a lot more than chips. The clinging of newly laundered synthetic fabrics is related to such sparks. All these phenomena involve electric charge and electrical interactions, one of naturersquo;s fundamental classes of interactions. In this chapter, wersquo;ll study the interactions among electric charges that are at rest in our frame of reference; we call these electrostatic interactions. They are governed by Coulombrsquo;s law and are most conveniently described using the concept of electric field. Wersquo;ll find that charge is quantized; it can have only certain values. The total electric charge in a system must be an integer multiple of the charge of a single electron. Electric charge obeys a conservation law: The total electric charge in a closed system must be constant. Electrostatic interactions hold atoms, molecules, and our bodies together, but they also are constantly trying to tear apart the nuclei of atoms. Wersquo;ll explore all these concepts in this chapter and the ones that follow.

Electric charge and Coulombrsquo;s law

Charge is simply a property of certain naturersquo;s elementary particles such as the electron ,proton, etc. It does not exist “outside” of these particles. It is so basic that it is difficult to describe except in that context of the effect that is ascribed to its existence.

There are two kinds of charge ,denoted arbitrarily as positive and negative. Since 1747 Benjamin Franklinrsquo;s discovery of charge , he also named positive negative electricity. We follow the convention: glass rod rubbing with silk brings positive charge ; plastic rod (sealing wax) rubbing with fur brings negative charge. In Section 29.5, we will define “positive” and “negative” on basic level through decay process of particle.

It is well known that all charges are equivalent, and algebraically additive. Like charges repel, unlike charges attract. Electricity neutrality of objects is the most common occurrence.

Charge are quantized, i.e., discrete. The fundamental charge is

=1.602176462(63)C

where C (Coulomb) is a derived unit for charge. In SI , A (Ampere) is a basic unit. 1C=1As. Is really fundamental? In quark model, while an quark bears fractional charge, and antiquarks have opposite charge.

Up quark down quark strange quark

- -

In this model, quark are confined. In experiments , B. Fairbank et al (1965, 1977-1981) found that on superconducting niobium ball of diameters 280 , masses kg, there exist fractional charges . But there is no further report. Perhaps it is hard to believe that the first event observed fractional charge might have happened at the same time as fundamental charge. In 1909 Millikan wrote in a conclusion section of a paper :”hellip;I have discarded one uncertain and unduplicated observation apparently upon a singly charge drop, which gave a value of the charge on the drop some 30 per cent lower than the final value of .” We admire Millikanrsquo;s attitude so seriously to a single datum, this very remark makes him the first one who observed the fractal charges . Anyway till now fractional charge is an open problem. Even the fractal charges present, they are still quantized, with one third as unit.

Charge is conserved in large-scale events or on the atomic and nuclear level. In microscopic world, every particle has its own antiparticle. They have equal mass, half-life but opposite charge (see Chapter 30 for details). Charge conjugate symmetry means that worlds and one with exchange of particles and antiparticles are indistinguishable.

Whatever has charge has mass. In other words, a particle of zero rest mass has zero charge.

In 1785 Charles Augustin de Coulomb (1736-1806) proposed a law later named after his name——Coulombrsquo;s law. The law reads that the force by a charge on charge is

== -

The constant k was determined by Coulomb torsion balance. Later Cavendish used the torsion balance to measure gravitational attraction.

k=

Where the constant is permittivity of free space, also called dielectric constant.

=8.854187817hellip;

The law hold only for point charges, so never approaches to zero. Physically a point may be of size about nanometer, Angstrom, or Fermi. For charge of finite size a single distance will be non-sense. In that case one may first consider Coulombrsquo;s law for pairs of volume elements and sum up or integrate force vectors for resultant force. Coulombrsquo;s law is for two-body. When there exist more than two point charges ,only two-body actions exist.

Similar to Newtonrsquo;s law of gravitation, Coulombrsquo;s law is an “action at a distance”. According to modern concept , action propagates with finite speed. Essential similarity between Coulombrsquo;s law and law of gravitation is that both of them are inverse-square laws though gravitation is much weaker. To examine the inverse square law may write as

And examine the deviation from 2. Earlier upper limits may list as 0.06 (John Robinson) ,

0.02 (Henry Cavendish). Modern experiments show

(2.73.1)

Coulombrsquo;s law is valid in a wide range. Macroscopic objects such as cable, we ourselves are made up by atoms or molecules mainly with Coulomb force rather than gravitation. Thanks to Coulomb action ,atoms can form molecule or electrons and nucleus can form atom . what is the case

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University Physics

Chapter 17 Electric Charge and Electric Field

When you scuff your shoes across a carpet, you can get zapped by an annoying spark of static electricity. That same spark could totally destroy the function of a computer chip. Lightning, the same phenomenon on a vast scale, can destroy a lot more than chips. The clinging of newly laundered synthetic fabrics is related to such sparks. All these phenomena involve electric charge and electrical interactions, one of naturersquo;s fundamental classes of interactions. In this chapter, wersquo;ll study the interactions among electric charges that are at rest in our frame of reference; we call these electrostatic interactions. They are governed by Coulombrsquo;s law and are most conveniently described using the concept of electric field. Wersquo;ll find that charge is quantized; it can have only certain values. The total electric charge in a system must be an integer multiple of the charge of a single electron. Electric charge obeys a conservation law: The total electric charge in a closed system must be constant. Electrostatic interactions hold atoms, molecules, and our bodies together, but they also are constantly trying to tear apart the nuclei of atoms. Wersquo;ll explore all these concepts in this chapter and the ones that follow.

Electric charge and Coulombrsquo;s law

Charge is simply a property of certain naturersquo;s elementary particles such as the electron ,proton, etc. It does not exist “outside” of these particles. It is so basic that it is difficult to describe except in that context of the effect that is ascribed to its existence.

There are two kinds of charge ,denoted arbitrarily as positive and negative. Since 1747 Benjamin Franklinrsquo;s discovery of charge , he also named positive negative electricity. We follow the convention: glass rod rubbing with silk brings positive charge ; plastic rod (sealing wax) rubbing with fur brings negative charge. In Section 29.5, we will define “positive” and “negative” on basic level through decay process of particle.

It is well known that all charges are equivalent, and algebraically additive. Like charges repel, unlike charges attract. Electricity neutrality of objects is the most common occurrence.

Charge are quantized, i.e., discrete. The fundamental charge is

=1.602176462(63)C

where C (Coulomb) is a derived unit for charge. In SI , A (Ampere) is a basic unit. 1C=1As. Is really fundamental? In quark model, while an quark bears fractional charge, and antiquarks have opposite charge.

Up quark down quark strange quark

- -

In this model, quark are confined. In experiments , B. Fairbank et al (1965, 1977-1981) found that on superconducting niobium ball of diameters 280 , masses kg, there exist fractional charges . But there is no further report. Perhaps it is hard to believe that the first event observed fractional charge might have happened at the same time as fundamental charge. In 1909 Millikan wrote in a conclusion section of a paper :”hellip;I have discarded one uncertain and unduplicated observation apparently upon a singly charge drop, which gave a value of the charge on the drop some 30 per cent lower than the final value of .” We admire Millikanrsquo;s attitude so seriously to a single datum, this very remark makes him the first one who observed the fractal charges . Anyway till now fractional charge is an open problem. Even the fractal charges present, they are still quantized, with one third as unit.

Charge is conserved in large-scale events or on the atomic and nuclear level. In microscopic world, every particle has its own antiparticle. They have equal mass, half-life but opposite charge (see Chapter 30 for details). Charge conjugate symmetry means that worlds and one with exchange of particles and antiparticles are indistinguishable.

Whatever has charge has mass. In other words, a particle of zero rest mass has zero charge.

In 1785 Charles Augustin de Coulomb (1736-1806) proposed a law later named after his name——Coulombrsquo;s law. The law reads that the force by a charge on charge is

== -

The constant k was determined by Coulomb torsion balance. Later Cavendish used the torsion balance to measure gravitational attraction.

k=

Where the constant is permittivity of free space, also called dielectric constant.

=8.854187817hellip;

The law hold only for point charges, so never approaches to zero. Physically a point may be of size about nanometer, Angstrom, or Fermi. For charge of finite size a single distance will be non-sense. In that case one may first consider Coulombrsquo;s law for pairs of volume elements and sum up or integrate force vectors for resultant force. Coulombrsquo;s law is for two-body. When there exist more than two point charges ,only two-body actions exist.

Similar to Newtonrsquo;s law of gravitation, Coulombrsquo;s law is an “action at a distance”. According to modern concept , action propagates with finite speed. Essential similarity between Coulombrsquo;s law and law of gravitation is that both of them are inverse-square laws though gravitation is much weaker. To examine the inverse square law may write as

And examine the deviation from 2. Earlier upper limits may list as 0.06 (John Robinson) ,

0.02 (Henry Cavendish). Modern experiments show

(2.73.1)

Coulombrsquo;s law is valid in a wide range. Macroscopic objects such as cable, we ourselves are made up by atoms or molecules mainly with Coulomb force rather than gravitation. Thanks to Coulomb action ,atoms can form molecule or electrons and nucleus can form atom . what is the case

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