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** Chapter 21. Electric Charge **

21.1. What is Physics? 21.2. Electric Charge 21.3. Conductors and Insulators 21.4. Coulomb's Law 21.5. Charge is Quantized 21.6. Charge is Conserved

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What is Physics?

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**What is Electric Charge?**

An intrinsic property of protons and electrons, which make up all matter, is electric charge. A proton has a positive charge, and an electron has a negative charge.

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**Properties of electric charge**

Two types of electric charge, positive and negative; a proton has a positive charge, and an electron has a negative charge. The SI unit for measuring the magnitude of electric charge is the coulomb (C). The electric charge is said to be quantized. The smallest amount of free charge is e=1.6×10-19 C. Any electric charge, q, occurs as integer multiples of the elementary charge e

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**Example 1 A Lot of Electrons**

How many electrons are there in one coulomb of negative charge? Solution The number N of electrons is

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**Continue on Properties of electric charge**

Two electrically charged objects exert a force on one another, called as electrostatic force : like charges repel and unlike charges attract each other.

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**Continue on Properties of electric charge**

It is possible to transfer electric charge from one object to another. Usually electrons are transferred, and the body that gains electrons acquires an excess of negative charge. The body that loses electrons has an excess of positive charge. During any process, the net electric charge of an entire isolated system remains constant (is conserved). This is referred to as the law of conservation of electric charge.

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**Conductors and Insulators**

Not only can electric charge exist on an object, but it can also move through an object. Substances that readily conduct electric charge are called electrical conductors. Materials that conduct electric charge poorly are known as electrical insulators. Semiconductors are materials that are intermediate between conductors and insulators

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**Charging by Contact and by Induction**

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**Example: Bacterial Contamination and Electrostatics**

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Checkpoint The figure shows five pairs of plates: A, B, and D are charged plastic plates and C is an electrically neutral copper plate. The electrostatic forces between the pairs of plates are shown for three of the pairs. For the remaining two pairs, do the plates repel or attract each other?

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Coulomb's Law The electrostatic force is directed along the line joining the charges, and it is attractive if the charges have unlike signs and repulsive if the charges have like signs. The magnitude F of the electrostatic force exerted by one point charge q1 on another point charge q2 is directly proportional to the magnitudes |q1| and |q2| of the charges and inversely proportional to the square of the distance r between them.

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Coulomb's Law The quantity ε0 , called the permittivity constant, sometimes appears separately in equations and is

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**Example 3 A Model of the Hydrogen Atom**

In the Bohr model of the hydrogen atom, the electron (–e) is in orbit about the nuclear proton (+e) at a radius of r=5.29×10–11 m, as Figure shows. Determine the speed of the electron, assuming the orbit to be circular.

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**THE FORCE ON A POINT CHARGE DUE TO TWO OR MORE OTHER POINT CHARGES**

There are three charges q1, q2 and q3.What would be the net force on q1 due to both q2 and q3? First, find the magnitude and direction of the force exerted on q1 by q2 (ignoring q3). Then, determine the force exerted on q1 by q3 (ignoring q2). The net force on q1 is the vector sum of these forces.

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**THE FORCE ON A POINT CHARGE DUE Many POINT CHARGES**

If we have n charged particles, they interact independently in pairs, and the force on any one of them, let us say particle 1, is given by the vector sum

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shell theorem A shell of uniform charge attracts or repels a charged particle that is outside the shell as if all the shell's charge were concentrated at its center. If a charged particle is located inside a shell of uniform charge, there is no net electrostatic force on the particle from the shell.

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Spherical Conductors If excess charge is placed on a spherical shell that is made of conducting material, the excess charge spreads uniformly over the (external) surface. If we remove negative charge from a spherical metal shell, the resulting positive charge of the shell is also spread uniformly over the surface of the shell.

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**Example Three Charges in a Plane**

Figure shows three point charges that lie in the x, y plane in a vacuum. Find the magnitude and direction of the net electrostatic force on q1.

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Sample Problem In Fig a, two identical, electrically isolated conducting spheres A and B are separated by a (center-to-center) distance a that is large compared to the spheres. Sphere A has a positive charge of , and sphere B is electrically neutral. Initially, there is no electrostatic force between the spheres. (Assume that there is no induced charge on the spheres because of their large separation.) (a) Suppose the spheres are connected for a moment by a conducting wire. The wire is thin enough so that any net charge on it is negligible. What is the electrostatic force between the spheres after the wire is removed? (b) Next, suppose sphere A is grounded momentarily, and then the ground connection is removed. What now is the electrostatic force between the spheres?

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Conceptual Questions In Figure the grounding wire is removed first, followed by the rod, and the sphere is left with a positive charge. If the rod were removed first, followed by the grounding wire, would the sphere be left with a charge? Account for your answer.

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2. A metallic object is given a positive charge by the process of induction, as illustrated in Figure (a) Does the mass of the object increase, decrease, or remain the same? Why? (b) What happens to the mass of the object if it is given a negative charge by induction? Explain.

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**3. Blow up a balloon and rub it against your shirt a number of times**

3.Blow up a balloon and rub it against your shirt a number of times. In so doing you give the balloon a net electric charge. Now touch the balloon to the ceiling. On being released, the balloon will remain stuck to the ceiling. Why? 4. A particle is attached to a spring and is pushed so that the spring is compressed more and more. As a result, the spring exerts a greater and greater force on the particle. Similarly, a charged particle experiences a greater and greater force when pushed closer and closer to another particle that is fixed in position and has a charge of the same polarity. In spite of the similarity, the charged particle will not exhibit simple harmonic motion on being released, as will the particle on the spring. Explain why not.

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