Chapter Summary

PREVIEW

In this chapter you will be introduced to the concepts of electric charge, electric forces and electric fields. You will use Coulomb's law to find the forces and fields associated with point charges and charged plates. You will also learn how to "map" electric field lines and how electric fields are affected by the presence of conductors.

QUICK REFERENCE

Important Terms

Electric charge An intrinsic property of protons (positive charge) and electrons (negative charge). It is found that like charges (same polarity) repel one another while unlike charges (opposite polarity) attract one another. The SI unit of charge is the coulomb (C). Electrical conductors Materials which allow electric charge to flow freely through them. Electrical insulators Materials which do not allow electric charge to flow freely through them. Coulomb's law The magnitude of the electrical force exerted by one point charge on another is directly proportional to the magnitudes of the charges and inversely proportional to the square of the distance between the charges. The direction of the force is along the line joining the charges and is repulsive for like charges and attractive for unlike charges. Electric field At a point in space, the electrostatic force experienced by a small test charge placed at that point divided by the charge itself. Electric field is a vector quantity. The SI unit of electric field is the newton per coulomb (N/C). Electric field lines A visual representation of the electric field. It can be viewed as a "map" providing information about the direction and strength of the electric field in various regions. Gaussian surface A hypothetical closed surface in the vicinity of an electric field or a charge distribution. The Gaussian surface may enclose a net charge. Electric flux The product of the magnitude of the normal component of the electric field at any point on a surface element and the area of the surface element. It is assumed that the magnitude of the normal component of the electric field is constant over the surface element. The SI unit of electric flux is the newton square meter per coulomb (N·m²/C). Gauss' Law The mathematical expression that relates the electric flux through a closed (Gaussian) surface to the net charge enclosed by the surface. Gauss' Law can be used to calculate the magnitude of the electric field surrounding charge distributions that possess spatial symmetry.

Equations

Coulomb's law for the magnitude of the force that one point charge exerts on a second point charge is written as

(18.1)

where q₁ and q₂ are the magnitudes of the two point charges, and r is the distance between them.

The electric field can be written

(18.2)

The magnitude of the electric field due to a point charge is

(18.3)

The magnitude of the electric field between the plates of a parallel plate capacitor is given by

(18.4)

The electric flux through a closed surface can be written as

(18.6)

where E is the magnitude of the electric field at a point on the surface, and f is the angle between the electric field and the normal at that point.

Gauss' Law for a closed surface is written as

(18.7)

where Q is the net charge enclosed by the surface and e ₀ is the permittivity of free space.