Resource Lesson
Gauss' Law
Printer Friendly Version
Qualitatively Gauss' Law is often stated as, "the net number of flux lines out of any closed surface containing a charge is proportional to the net charge inside the surface" or
But what is meant by the term electric flux, Φ? These are electric field lines penetrating a surface. If a field line enters the surface its value can be thought of as -1 while a field line existing the surface can be thought of as +1. The unit for flux is a Nm
^{2}
/C.
Isolated
positive charges
are sometimes called
sources
since all of their field lines begin within the surface while isolated
negative charges
are sometimes called
sinks
since all of their field lines enter the surface.
positive isolated charge
"+16" flux lines
arrows point out
negative isolated charge
"-16" flux lines
arrows point in
If the surface encloses a mixture of charges, the number of flux lines is equal to the net, or sum, of the field lines entering and/or exiting the surface.
8 field lines leave and 6 field lines enter
(notice that 8 field lines are always inside the surface and are not counted)
net flux = +2 telling us that the positive charge is larger
Remember that the relative strength of an electric field can be represented pictorially as a proportional number of field lines. If one charge has twice the magnitude of another, it would have two times as many field lines.
Dot Product
When calculating the magnitude of the electric flux passing through a surface, the formula is
where
E is the magnitude of the electric field,
A is the cross-sectional area of the plane, and
θ is the angle measured between the electric field lines and the normal to the area (which is called the area vector).
Remember that dot products produce scalar answers. So your results will no longer have a direction, only magnitude. That is, you will not be asked to find the components of the number of flux lines
In the top diagram the angle between the field lines equals 0º, so Φ = EA cos(0) = EA, its maximum value.
In the middle diagram the angle between the field lines equals 45º, so Φ = EA cos(45) = E(0.707A).
In the final diagram the angle between the field lines equals 90º, so Φ = EA cos(90) = 0.
To use Gauss' Law to calculate the electric field in a region, we choose a convenient Gaussian surface whose "edges or sides" lie either perpendicular or parallel to the field lines emanating from the charged object. We will only be responsible for highly symmetrical objects: point charges, charged wires/rods/cylinders, and sheets/disks of charge. We will begin our study with point charges.
Point Charges
Notice that by taking our Gaussian surface to also be a sphere, the field lines will always pass perpendicular to its surface [θ = 90º and cos(90º) = 1] so we can write Gauss' Law as
Charged Plane
Suppose we now look at a uniformly charged plane; that is, a surface
Related Documents
Lab:
Labs -
Aluminum Foil Parallel Plate Capacitors
Labs -
Electric Field Mapping
Labs -
Electric Field Mapping 2
Labs -
Mass of an Electron
Labs -
RC Time Constants
Resource Lesson:
RL -
A Comparison of RC and RL Circuits
RL -
Capacitors and Dielectrics
RL -
Continuous Charge Distributions: Charged Rods and Rings
RL -
Continuous Charge Distributions: Electric Potential
RL -
Coulomb's Law: Beyond the Fundamentals
RL -
Coulomb's Law: Suspended Spheres
RL -
Derivation of Bohr's Model for the Hydrogen Spectrum
RL -
Dielectrics: Beyond the Fundamentals
RL -
Electric Field Strength vs Electric Potential
RL -
Electric Fields: Parallel Plates
RL -
Electric Fields: Point Charges
RL -
Electric Potential Energy: Point Charges
RL -
Electric Potential: Point Charges
RL -
Electrostatics Fundamentals
RL -
Famous Experiments: Millikan's Oil Drop
RL -
LC Circuit
RL -
Parallel Plate Capacitors
RL -
Shells and Conductors
RL -
Spherical, Parallel Plate, and Cylindrical Capacitors
Review:
REV -
Drill: Electrostatics
REV -
Electrostatics Point Charges Review
Worksheet:
APP -
The Birthday Cake
APP -
The Electrostatic Induction
CP -
Coulomb's Law
CP -
Electric Potential
CP -
Electrostatics: Induction and Conduction
NT -
Electric Potential vs Electric Potential Energy
NT -
Electrostatic Attraction
NT -
Lightning
NT -
Photoelectric Effect
NT -
Potential
NT -
Van de Graaff
NT -
Water Stream
WS -
Capacitors - Connected/Disconnected Batteries
WS -
Charged Projectiles in Uniform Electric Fields
WS -
Combinations of Capacitors
WS -
Coulomb Force Extra Practice
WS -
Coulomb's Law: Some Practice with Proportions
WS -
Electric Field Drill: Point Charges
WS -
Electric Fields: Parallel Plates
WS -
Electric Potential Drill: Point Charges
WS -
Electrostatic Forces and Fields: Point Charges
WS -
Electrostatic Vocabulary
WS -
Parallel Reading - The Atom
WS -
Standard Model: Particles and Forces
TB -
Advanced Capacitors
TB -
Basic Capacitors
TB -
Electric Field Strength vs Electric Potential
PhysicsLAB
Copyright © 1997-2018
Catharine H. Colwell
All rights reserved.
Application Programmer
Mark Acton