Week 2

Other Notes

Ch. 5 Equations and Key Terms

Coulomb’s law F⃗ 12(r)=14πε0q1q2r212rˆ12

Superposition of electric forces F⃗ (r)=14πε0Q∑i=1Nqir2irˆi

Electric force due to an electric field F⃗ =QE⃗

Electric field at point P E⃗ (P)≡14πε0∑i=1Nqir2irˆi

Field of an infinite wire E⃗ (z)=14πε02λzkˆ

Field of an infinite plane E⃗ =σ2ε0kˆ

Dipole moment p⃗ ≡qd⃗

Torque on dipole in external E-field τ⃗ =p⃗ ×E⃗

Key Terms

charging by induction

process by which an electrically charged object brought near a neutral object creates a charge separation in that object

conduction electron

electron that is free to move away from its atomic orbit

conductor

material that allows electrons to move separately from their atomic orbits; object with properties that allow charges to move about freely within it

continuous charge distribution

total source charge composed of so large a number of elementary charges that it must be treated as continuous, rather than discrete

coulomb

SI unit of electric charge

Coulomb force

another term for the electrostatic force

Coulomb’s law

mathematical equation calculating the electrostatic force vector between two charged particles

dipole

two equal and opposite charges that are fixed close to each other

dipole moment

property of a dipole; it characterizes the combination of distance between the opposite charges, and the magnitude of the charges

electric charge

physical property of an object that causes it to be attracted toward or repelled from another charged object; each charged object generates and is influenced by a force called an electric force

electric field

physical phenomenon created by a charge; it “transmits” a force between a two charges

electric force

noncontact force observed between electrically charged objects

electron

particle surrounding the nucleus of an atom and carrying the smallest unit of negative charge

electrostatic attraction

phenomenon of two objects with opposite charges attracting each other

electrostatic force

amount and direction of attraction or repulsion between two charged bodies; the assumption is that the source charges have no acceleration

electrostatic repulsion

phenomenon of two objects with like charges repelling each other

electrostatics

study of charged objects which are not in motion

field line

smooth, usually curved line that indicates the direction of the electric field

field line density

number of field lines per square meter passing through an imaginary area; its purpose is to indicate the field strength at different points in space

induced dipole

typically an atom, or a spherically symmetric molecule; a dipole created due to opposite forces displacing the positive and negative charges

infinite plane

flat sheet in which the dimensions making up the area are much, much greater than its thickness, and also much, much greater than the distance at which the field is to be calculated; its field is constant

infinite straight wire

straight wire whose length is much, much greater than either of its other dimensions, and also much, much greater than the distance at which the field is to be calculated

insulator

material that holds electrons securely within their atomic orbits

ion

atom or molecule with more or fewer electrons than protons

law of conservation of charge

net electric charge of a closed system is constant

linear charge density

amount of charge in an element of a charge distribution that is essentially one-dimensional (the width and height are much, much smaller than its length); its units are C/m

neutron

neutral particle in the nucleus of an atom, with (nearly) the same mass as a proton

permanent dipole

typically a molecule; a dipole created by the arrangement of the charged particles from which the dipole is created

permittivity of vacuum

also called the permittivity of free space, and constant describing the strength of the electric force in a vacuum

polarization

slight shifting of positive and negative charges to opposite sides of an object

principle of superposition

useful fact that we can simply add up all of the forces due to charges acting on an object

proton

particle in the nucleus of an atom and carrying a positive charge equal in magnitude to the amount of negative charge carried by an electron

static electricity

buildup of electric charge on the surface of an object; the arrangement of the charge remains constant (“static”)

superposition

concept that states that the net electric field of multiple source charges is the vector sum of the field of each source charge calculated individually

surface charge density

amount of charge in an element of a two-dimensional charge distribution (the thickness is small); its units are C/m2

volume charge density

amount of charge in an element of a three-dimensional charge distribution; its units are C/m3

Ch. 6 Equations and Key Terms

Definition of electric flux, for uniform electric field Φ=E→⋅A→→EAcosθ

Electric flux through an open surface Φ=∫SE→⋅nˆdA=∫SE→⋅dA→

Electric flux through a closed surface Φ=∮SE→⋅nˆdA=∮SE→⋅dA→

Gauss’s law Φ=∮SE→⋅nˆdA=qencε0

Gauss’s Law for systems with symmetry Φ=∮SE→⋅nˆdA=E∮SdA=EA=qencε0

The magnitude of the electric field just outside the surface of a conductor E=σε0

Key Terms

area vector

vector with magnitude equal to the area of a surface and direction perpendicular to the surface

cylindrical symmetry

system only varies with distance from the axis, not direction

electric flux

dot product of the electric field and the area through which it is passing

flux

quantity of something passing through a given area

free electrons

also called conduction electrons, these are the electrons in a conductor that are not bound to any particular atom, and hence are free to move around

Gaussian surface

any enclosed (usually imaginary) surface

planar symmetry

system only varies with distance from a plane

spherical symmetry

system only varies with the distance from the origin, not in direction

Ch. 7 Equations and Key Terms

Potential energy of a two-charge system U(r)=kqQr

Work done to assemble a system of charges W12⋯N=k2∑iN∑jNqiqjrijfori≠j

Potential difference ΔV=ΔUqorΔU=qΔV

Electric potential V=Uq=−∫PRE→⋅dl→

Potential difference between two points ΔVBA=VB−VA=−∫BAE→⋅dl⃗

Electric potential of a point charge V=kqr

Electric potential of a system of point charges VP=k∑1Nqiri

Electric dipole moment p⃗ =qd⃗

Electric potential due to a dipole VP=kp⃗ ⋅rˆr2

Electric potential of a continuous charge distribution VP=k∫dqr

Electric field components Ex=−∂V∂x,Ey=−∂V∂y,Ez=−∂V∂z

Del operator in Cartesian coordinates ∇⃗ =iˆ∂∂x+jˆ∂∂y+kˆ∂∂z

Electric field as gradient of potential E→=−∇⃗ V

Del operator in cylindrical coordinates ∇⃗ =rˆ∂∂r+φˆ1r∂∂φ+zˆ∂∂z

Del operator in spherical coordinates ∇⃗ =rˆ∂∂r+θˆ1r∂∂θ+φˆ1rsinθ∂∂φ

Key Terms

Key Terms

electric dipole

system of two equal but opposite charges a fixed distance apart

electric dipole moment

quantity defined as p⃗ =qd⃗ for all dipoles, where the vector points from the negative to positive charge

electric potential

potential energy per unit charge

electric potential difference

the change in potential energy of a charge q moved between two points, divided by the charge.

electric potential energy

potential energy stored in a system of charged objects due to the charges

electron-volt

energy given to a fundamental charge accelerated through a potential difference of one volt

electrostatic precipitators

filters that apply charges to particles in the air, then attract those charges to a filter, removing them from the airstream

equipotential line

two-dimensional representation of an equipotential surface

equipotential surface

surface (usually in three dimensions) on which all points are at the same potential

grounding

process of attaching a conductor to the earth to ensure that there is no potential difference between it and Earth

ink jet printer

small ink droplets sprayed with an electric charge are controlled by electrostatic plates to create images on paper

photoconductor

substance that is an insulator until it is exposed to light, when it becomes a conductor

Van de Graaff generator

machine that produces a large amount of excess charge, used for experiments with high voltage

voltage

change in potential energy of a charge moved from one point to another, divided by the charge; units of potential difference are joules per coulomb, known as volt

xerography

dry copying process based on electrostatics