Concept Summary

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Topic | Discussion | Learning Aids
The coulomb (C) | 18.1 THE ORIGIN OF ELECTRICITY There are two kinds of electric charge: positive and negative. The SI unit of electric charge is the coulomb (C). The magnitude of the charge on an electron or a proton is |
Magnitude of charge on electron or proton |

Since the symbol e denotes a magnitude, it has no algebraic sign. Thus, the electron carries a charge of − e, and the proton carries a charge of + e.
Charge is quantized | The charge on any object, whether positive or negative, is quantized, in the sense that the charge consists of an integer number of protons or electrons. |
Law of conservation of electric charge | 18.2 CHARGED OBJECTS AND THE ELECTRIC FORCE The law of conservation of electric charge states that the net electric charge of an isolated system remains constant during any process. |
Electric repulsion and attraction | Like charges repel and unlike charges attract each other. |
Conductor | 18.3 CONDUCTORS AND INSULATORS An electrical conductor is a material, such as copper, that conducts electric charge readily. |
Insulator | An electrical insulator is a material, such as rubber, that conducts electric charge poorly. |
Charging by contact | 18.4 CHARGING BY CONTACT AND BY INDUCTION Charging by contact is the process of giving one object a net electric charge by placing it in contact with an object that is already charged. |
Charging by induction | Charging by induction is the process of giving an object a net electric charge without touching it to a charged object. |
Point charge | 18.5 COULOMB’s LAW A point charge is a charge that occupies so little space that it can be regarded as a mathematical point. Coulomb’s law gives the magnitude F of the electric force that two point charges q1 and q2 exert on each other: |
Coulomb’s law |

| (18.1)

where and are the magnitudes of the charges and have no algebraic sign. The term k is a constant and has the value . The force specified by Equation 18.1 acts along the line between the two charges.
Permittivity of free space | The permittivity of free space is defined by the relation

Use Self-Assessment Test 18.1 to evaluate your understanding of Sections 18.1, 18.2, 18.3, 18.4 and 18.5 .

| 18.6 THE ELECTRIC FIELD The electric field at a given spot is a vector and is the electrostatic force experienced by a very small test charge q0 placed at that spot divided by the charge itself: |
Electric field |

| (18.2)

| The direction of the electric field is the same as the direction of the force on a positive test charge. The SI unit for the electric field is the newton per coulomb (N/C). The source of the electric field at any spot is the charged objects surrounding that spot.
The magnitude of the electric field created by a point charge q is
Electric field of a point charge |

| (18.3)

where |q| is the magnitude of the charge and has no algebraic sign and r is the distance from the charge. The electric field points away from a positive charge and toward a negative charge.
For a parallel plate capacitor that has a charge per unit area of on each plate, the magnitude of the electric field between the plates is
Electric field of a parallel plate capacitor |

| (18.4)

Electric field lines Direction of electric field Strength of electric field | 18.7 ELECTRIC FIELD LINES Electric field lines are lines that can be thought of as a “map,” insofar as the lines provide information about the direction and strength of the electric field. The lines are directed away from positive charges and toward negative charges. The direction of the lines gives the direction of the electric field, since the electric field vector at a point is tangent to the line at that point. The electric field is strongest in regions where the number of lines per unit area passing perpendicularly through a surface is the greatest—that is, where the lines are packed together most tightly. |
Excess charge carried by a conductor at equilibrium | 18.8 THE ELECTRIC FIELD INSIDE A CONDUCTOR: SHIELDING Excess negative or positive charge resides on the surface of a conductor at equilibrium under electrostatic conditions. In such a situation, the electric field at any point within the conducting material is zero, and the electric field just outside the surface of the conductor is perpendicular to the surface. |
| 18.9 Gauss’ LAW The electric flux through a surface is related to the magnitude E of the electric field, the area A of the surface, and the angle that specifies the direction of the field relative to the normal to the surface: |
Electric flux |

| (18.6)

Gauss’ law states that the electric flux through a closed surface (a Gaussian surface) is equal to the net charge Q enclosed by the surface divided by , the permittivity of free space:
Gauss’ law |

| (18.7)

Use Self-Assessment Test 18.2 to evaluate your understanding of Sections 18.6, 18.7, 18.8 and 18.9 .

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