Concept Summary

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Topic | Discussion | Learning Aids
Work and electric potential energy | 19.1 POTENTIAL ENERGY When a positive test charge +q0 moves from point A to point B in an electric field, work WAB is done by the electric force. The work equals the electric potential energy (EPE) at A minus that at B: |

| (19.1)

Path independence | The electric force is a conservative force, so the path along which the test charge moves from A to B is of no consequence, for the work WAB is the same for all paths. |
| 19.2 THE ELECTRIC POTENTIAL DIFFERENCE The electric potential V at a given point is the electric potential energy of a small test charge q0 situated at that point divided by the charge itself: |
Electric potential |

| (19.3)

| The SI unit of electric potential is the joule per coulomb (J/C), or volt (V). The electric potential difference between two points A and B is |
Electric potential difference |

| (19.4)

Acceleration of positive and negative charges | A positive charge accelerates from a region of higher potential toward a region of lower potential. Conversely, a negative charge accelerates from a region of lower potential toward a region of higher potential. |
Electron volt | An electron volt (eV) is a unit of energy. The relationship between electron volts and joules is . |
| The total energy E of a system is the sum of its translational and rotational kinetic energies, gravitational potential energy (mgh), elastic potential energy , and electric potential energy (EPE): |
Total energy Conservation of energy |

| If external nonconservative forces like friction do no net work, the total energy of the system is conserved. That is, the final total energy Ef is equal to the initial total energy E0; . |
| 19.3 THE ELECTRIC POTENTIAL DIFFERENCE CREATED BY POINT CHARGES The electric potential V at a distance r from a point charge q is |
Electric potential of a point charge |

| (19.6)

| where . This expression for V assumes that the electric potential is zero at an infinite distance away from the charge. |
Total electric potential | The total electric potential at a given location due to two or more charges is the algebraic sum of the potentials due to each charge. |
Total potential energy of a group of charges | The total potential energy of a group of charges is the amount by which the electric potential energy of the group differs from its initial value when the charges are infinitely far apart. It is also equal to the work required to assemble the group, one charge at a time, starting with the charges infinitely far apart. |

Use Self-Assessment Test 19.1 to evaluate your understanding of Sections 19.1, 19.2 and 19.3

Equipotential surface | 19.4 EQUIPOTENTIAL SURFACES AND THEIR RELATION TO THE ELECTRIC FIELD An equipotential surface is a surface on which the electric potential is the same everywhere. The electric force does no work as a charge moves on an equipotential surface, because the force is always perpendicular to the displacement of the charge. |
| The electric field created by any group of charges is everywhere perpendicular to the associated equipotential surfaces and points in the direction of decreasing potential. |
Relation between the electric field and the potential gradient | The electric field is related to two equipotential surfaces by |

| (19.7a)

| where is the potential difference between the surfaces and is the displacement. The term is called the potential gradient. |
A capacitor | 19.5 CAPACITORS AND DIELECTRICS A capacitor is a device that stores charge and energy. It consists of two conductors or plates that are near one another, but not touching. The magnitude q of the charge on each plate is given by |
Relation between charge and potential difference |

| (19.8)

| where V is the magnitude of the potential difference between the plates and C is the capacitance. The SI unit for capacitance is the coulomb per volt (C/V), or farad (F). |
| The insulating material included between the plates of a capacitor is called a dielectric. The dielectric constant of the material is defined as |
Dielectric constant |

| (19.9)

| where E0 and E are, respectively, the magnitudes of the electric fields between the plates without and with a dielectric, assuming the charge on the plates is kept fixed. |
| The capacitance of a parallel plate capacitor filled with a dielectric is |
Capacitance of a parallel plate capacitor |

| (19.10)

| where is the permittivity of free space, A is the area of each plate, and d is the distance between the plates. |
| The electric potential energy stored in a capacitor is |
Energy stored in a capacitor |

| (19.11a–c)

The energy density is the energy stored per unit volume and is related to the magnitude E of the electric field as follows:
Energy density |

| (19.12)

Use Self-Assessment Test 19.2 to evaluate your understanding of Sections 19.4 and 19.5.

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