# Electrostatics

Electricity in one form or another is involved in just about everything around. It is in the static electricity that builds up when you shuffle your feet across a rug; and it is what holds atoms together to form molecules. Electrostatics refers to electricity at rest. It involves electric charges, the forces between them, and their behavior in materials.

### Electrical Forces and Charges

We are under a tremendous force, billions of times stronger than gravity, strong enough to compress us to the thickness of a piece of paper. There is also a repelling force that is also many billons times stronger than gravity, that balances out this compressive force on us. The two forces balance each other out and so have no noticeable effect on us. These forces are electrical forces.

Electrical forces rise from dormant particles. The protons in the nucleus of an atom attract the electrons and hold them in orbit just as the sun holds the planets in orbit. Electrons are attracted to protons but not other electrons. This attracting and repelling behavior can be attributed to charge. Names attributed to various charges are arbitrary. By convention, electrons are described as negatively charged and protons positively charge. Neutrons have no charge and are neither attracted nor repelled by charged particles. The fundamental rule at the base of all electrical phenomena is:

### Conservation of Charge

If the total positive charges do not balance the total negative charges exactly then a charged atom results which is called an ion. A positive ion (cation) has a positive charge, meaning it lost one or more electrons. A negative ion (anion) has a negative charge, meaning it has gained electrons.

An object that has unequal numbers of electrons and protons is electrically charged. If it has more electrons than protons the object is negativity charged. If it has fewer electrons than protons than it is positively charged.

Electrons are neither created nor destroyed but are simply transferred from one material to another. Charge is always conserved. This principle is referred to as the Principle of Conservation of Charge.

### Coulomb’s Law

As with the law of gravitation, the electrical force between any two objects obeys a similar inverse square relationship with distance. Coulomb’s law states that for charges particles or objects that are small compared with the distance between them that, the force between the charges varies directly as the product of the charges and inversely as the square the distance between them. Coulomb’s law can be expressed as:

### F = kQ₁Q₂/d²

d is the distance between the charged particles; Q represents the quantity of charges of particles 1 and 2; k is the proportionality constant.

The SI unit of charge is the Coulomb, abbreviated C. The charge of one Coulomb (1 C) is the charge of 6.24 billion billon (6.24 x 10¹⁸) electrons. This represents the charge that passes through a common 100-watt light bulb in about 1 second.

The proportionality constant k in Coulomb’s law is similar to G in Newton’s law of gravitation. Instead of being a very small number like G, the electrical proportionality constant k is a very large number. Rounded off it equals

k = 9,000,000,000 N* m²/c²

k = 9.0 x 10⁹N*m²/c²

Theunits N*m²/C² convert the right-hand side of the equation to the unit of force, the Newton (N). If a pair of charges of 1 Coulomb each were 1 meter apart, the force of repulsion between the two charges would be 9 billion Newtons. That would be more than 10X the weight of a battleship! Fortunately, such net charge do not exist in our everyday environment.

### Conductors and Insulators

Electrons are more easily moved around in some materials than others. Materials whose electrons are free to roam about in the material are good conductors of electricity. Metals are good conductors. Electrons in other materials such as rubber and glass are tightly bound and are not free to wander around. These materials are poor conductors of electricity and are referred to as insulatorsSemi-conductors are materials that may be made to behave some times as insulators and sometimes as conductors. Silicon in its pure crystalline form is a good insulator but exhibits good conductivity when certain derivatives are added to the crystals. Thin layers of semi-conducting material sandwiched together make up transistors, which are used in electrical applications. At temperatures near absolute zero, certain metals acquire infinite conductivity, which means they have zero resistance to the flow of charge. These are referred to as super conductors. Super conductivity at high temperature above 100° K have been found in a variety of none metallic compounds in recent years.

### Friction and Contact

Electrons can be transferred from one material to another by simple touching. After touching, the charge will spread to all parts of its surface because the like charges repel each other. If it is a poor conductor it may be necessary to touch the rod at several places on the object in order to get a more or less uniform distribution of charges.

### Induction

If a charged object is brought near a conducting surface without physical contact, electrons will move in the conducting surface. A charge is said to have been induced. If a negative charge is brought near two objects that are touching one another, the object closest to the negatively charged object will develop a net positive charge while the other object in contact with it will develop a negative net charge. The two objects touching one another can then be separated and they will retain their initial charged until touched. The ground is an infinite reservoir for electrical charge. When a metal surface is touched with a finger, charges are allowed to move off or onto a conductor in a process known as grounding.

Charging by induction occurs during thunderstorms. The negatively charged bottoms of clouds induce a positive charge on the surface of the Earth below. Most lightening is an electrical discharge between oppositely charged parts of clouds. The kind we are most familiar with is the electrical discharge between the clouds and the oppositely charged ground below.

### Polarization

Charging by induction is not restricted to conductors. A charged rod is brought near an insulator and there are no free electrons to migrate throughout the insulating material. Instead there is a rearrangement of the position of charges within the atoms and molecules themselves. One side of the atom of the molecule is induced to be slightly more positive or negative than the opposite side. The atom or molecule is said to be electrically polarized.

Many molecules, water for example, are electrically polarized in their normal states. The distribution of the electrical charges is not perfectly even. There is a little more negative charge on one side of the molecule than on the other. Such molecules are said to be electric dipoles.

### Review Questions:

1. Two charges, one of 3.0 x 10-8 C and the other -4.0 x 10-8 C, are separated by 6.0 x 10-3 m. What is the force of one on the other?

0.30 N

2. Consider a line of charges; 8.0 uC, -12 uC at 2.0 cm, and 10 uC at 4.0 cm. What is the force on the third charge due to the other two charges?

The force on Q3 due to Q2 is attractive and the magnitude is 2700 N.     The resultant force is 2700 - 450 N = 2250 N. This force is attractive and toward the left.

3. A positive charge of 3.6 x 10-5 C and a negative charge of -2.4 x 10-5 C are 0.034 m apart. What is the force between the two particles?

6.7 x 10*2 N

4. The force between two objects is 64 N. One object has a positive charge of 1.4 x 10-6 C, while the other has a negative charge of 1.8 x 10-6 C. How far apart are the objects?

1.2 x 10*-2 m

5. Two negative charges of 4.2 x 10-8 C are separated by 0.46 m. What is the magnitude of the force acting on each object?

7.5 x 10* -5 N

6. Two objects exert a force of 4.2 N on each other. The distance between the objects is 0.36 m. The charge on one object is 2.8 x 10-9 C. What is the charge on the second object?

0.022 C

7. Two objects, one having twice the charge of the other, are separated by 0.78 m and exert a force of 3.8 x 103 N. What is the magnitude of charge on each object?

3.6 x 10* -4 C and 7.2 x 10* -4 C

8. A negative charge of -2.0 x 10-4 C and a positive charge of 8.0 x 10-4 C are separated by 0.30 m. What is the force between the two charges?

1.6 x 10*4 N

9. How many excess electrons are on a ball with a charge of -4.00 x 10-17 C?

2.5 x 10*2 electrons

10. A positive charge of 3.0 uC is pulled on by two negative charges. One, -2.0 uC is 0.050 m to the north and the other, -4.0 uC, is 0.030 m to the south. What total force is exerted on the positive charge?

F = F2 + F1= (1.2 x 10*2 N) - (2.2 x 10*1 N) = 98 N, south

### Honors

11. Three charges are arranged in the form of an equilateral triangle. The first charge is 2.0 x 10-6 C. The second charge is -3.0 x 10-6 C is two meters away from charge one horizontally. The third charge is 5.0 x 10-6 C and is located centrally above the first two charges.

Fx = 0.0281 N; Fy = -0.0097 z

12. Three particles are placed in a line. The left particle has a charge of -67 uC, the middle +45 uC, and the right, -83 uC. The middle particle is 72 cm from each of the others. What is the net force on the right particle?

41 N, left

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