Electric Charges and Fields

• Chapter 22 discusses electric fields.

Assessment Standards

• Class Participation and Homework: 20%
• Midterm Exam: 40%
• Final Exam: 40%
• Bonus Problems Report available

Properties of Electric Charge

• Benjamin Franklin (1706-1790) discovered two kinds of electric charges: positive and negative.
• Like charges repel one another, and unlike charges attract one another.
• The net charge of a closed system never changes; this principle is known as the Conservation of Charge.
• Robert Millikan (1868-1953) discovered that electric charge always occurs as some integral multiple of a fundamental amount of charge e.
• Electric charge q is quantized according to the equation q = Ne.
• An electron has a charge of -e and a mass of me.
• A proton has a charge of +e and a mass of 1836me.
• A neutron has a charge of 0 and a mass of 1839me.
• The elementary charge e is equal to 1.602 x 10^-19 C, where C stands for Coulomb, the SI unit of charge.
• The mass of an electron (me) is 9.11 x 10^-31 kg.
• The net charge is always a multiple of e, represented as Qnet = Ne.

Insulators and Conductors

• Electric conductors are materials in which electric charges move freely, such as metals like Gold, Copper, and Silver.
• Electric insulators are materials in which electric charges cannot move freely, such as Glass, Plastic, and Wood.
• Semiconductors are materials with electrical properties between those of insulators and conductors, such as Silicon and Germanium.
• Metals have free electrons, these electrons are not completely free; they are bound to the metal as a whole.
• Ionic solutions are conductors because ions can move. Salt water contains Na+ and Cl-, H+ and OH-.
• It is hard to charge objects when humidity is high because a thin water film forms on all surfaces and charge can move.
• Pure water is a good insulator.
• Water is often regarded as a conductor, one should avoid touching electronic components with wet hands.
• Pure water consists almost entirely of intact water molecules so they don't carry a net charge.
• There are only small amounts of ion concentrations (H+ and OH-), however, tap water is not pure: it contains dissolved minerals.
• These minerals greatly increase the concentration of ions, making tap water a conductor. The human body contains many ions which is why it is a conductor.
• Air is a reliable insulator because most of its molecules are electrically neutral and do not carry a charge when they move.
• Air does contain a few ions, ionization of air molecules can occur through radioactive decay or cosmic rays.

Charging Objects by Rubbing

• To charge a neutral object, charge must be transferred from another object.
• Large organic molecules can break into charged parts (ions).
• The charged parts can be physically transferred.
• Triboelectric charging occurs when charging by rubbing. Initially, both objects neutral: Qrod=0 and Qfur=0.
• After rubbing, the charges change: Qrod0.
• During the process, charge is conserved: Qrod + Qfur = 0.
• The triboelectric series lists materials according to their tendency to gain or lose electrons.
• Amber/resin gains electrons while fur loses electrons.
• The word "electricity" comes from the Greek word for amber (elektron).

Charging Objects

• Charging by rubbing: amber is charged by friction and some charge is transferred between the amber and cloth.
• Charging by contact occurs when a charged object touches a neutral object, transferring some of its charge.
• Charging by induction works only if the sphere is a conductor that is grounded, allowing electrons to leave the sphere and go to the earth. Removing the wire and rod results in a positively charged sphere.
• Grounding is achieved by connecting a conductor to the Earth, which acts as a large reservoir for electric charge.
• Ground = the Earth, which is a good conductor.
• Grounding prevents the build-up of static charge by discharging a conductor.
• Grounding conductors can prevent static charge buildup.
• Even small amounts of charge accumulation are dangerous.

Applications of Electrostatics

• Photocopiers (and laser printers) use electrostatics to create images on paper.
• Charging: A selenium-coated aluminum drum is given a positive charge by a rotating wire under an electrode.
• Exposure: The image of the document to be copied is projected onto the drum.
• Selenium is photoconductive, acting as an insulator until exposed to light, at which point it becomes a conductor.
• The drum is initially in darkness.
• The areas of the drum exposed to light become conductive, allowing electrons to neutralize the positive charge in those areas.
• Areas not exposed to light remain positively charged.
• Developing: The drum comes into contact with toner, black powder that is negatively charged.
• Toner particles are attracted to the positively charged areas of the drum but are repelled by the uncharged areas, forming a visible image.
• Transfer: A sheet of paper is given a strong positive charge on its back.
• The toner particles from the drum are attracted to the paper, transferring the image.
• Fusing: The paper passes through heated rollers, melting the toner and permanently bonding it to the paper.

Polarization

• Polarization occurs when the distribution of electric charge within a molecule or object is uneven.
• Paper bits are polarized by induction.

Coulomb's Law

• Charles Coulomb (1736-1806) measured the magnitudes of the electric forces between charged objects using the torsion balance, which he invented.
• Coulomb's Law quantifies the electric force (Fe) between two point charges (q1 and q2) separated by a distance r: F = ke * (|q1*q2|/r^2).
• ke represents Coulomb's constant with a value of 8.9875 x 10^9 N·m²/C².
• The constant ke is related to the permittivity of free space (ε0= 8.8542 × 10-12 C²/ N·m²), by the formula ke= 1/(4πε0).
• 1C of charge is approximately equal to the charge of 6.24 × 10^18 electrons or protons.
• Coulomb’s law predicts force between two point charges
• Point charge is a point-like object with a nonzero electric charge
• The force exerted by one point charge on another acts along the line joining the charges.
• The force varies inversely as the square of the distances separating the charges and is proportional to the product of the charges.
• The force is repulsive if the charges have the same sign and attractive if the charges have opposite signs
• Coulomb's Law expressed in vector form for the electric force exerted by a charge q₁ on a second charge q2, written F12, is F12=ke * (q1q2/r^2) r̂, where r̂ is a unit vector directed from q₁ to q2.

Electric Field

• The electric field E at a point in space is defined as the electric force Fe acting on a positive test charge q0 placed at that point divided by the magnitude of the test charge: E = Fe/q0.
• Gravity = (GmM)/r²
• Electric Force = k(qQ)/r²
• Gravitational field is always parallel to gravitational field (m>0)
• Electric force can be either parallel (q>0) or antiparallel (q<0) to electric field
• Electrolocation is the ability of certain animals and fishes to produce/sense electric fields.

Electric Field of a Point Charge

• Electric field of a point charge is E= k|Q|/r²
• Principle of superposition: electric field at any point is the vector sum of the fields at that point caused by each charge separately
• If Q>0, the field points away from Q (radially outward)
• If Q0
• The number of lines drawn leaving a positive charge or approaching a negative charge is proportional to the magnitude of the charge.
• No two field lines can cross.
• The total electric field at any point due to a group of charges equals the vector sum of the electric fields of the individual charges.

Electric Dipole

• Electric Field of a Dipole E = E₁ + E₂
• Electric Field of a Dipole E≈ke (2qa/ y³)
• Two point charges with equal and opposite charges creates an electric dipole
• Close to each of the charges (far from the other charge) field is strong looks like that of a single point charge
• Many molecules are dipoles
• An example of electric dipole molecules is HCl molecule
• If F=qE, then τ=qE r sine (where is the angle between E and r)
• Let d=distance between two charges
• Electric Dipole Moment P=qd to characterize charge/distance
• τ=pE sine or t=p x E is torque
• Recall that AW=-AU, AW=Fr=Fr cos0=qEd cose, ∆U=-qd E cos
• U = - p-E is the potential energy of a dipole in an electric field

Electric Fields in Conductors

• For a uniformly distributed positive charge Q over the surface of a spherical shell, the electric field inside the shell is zero.
• Positive charge: lines must start on sphere
• Radial symmetry: lines must be radial everywhere
• Electric Field inside the Shell is ZERO!
• Electric field is zero inside a conductor in electrostatic equilibrium

Electrostatic Equilibrium

• Conductor: free charges, can move far, easily polarized.
• In static equilibrium, there is no net motion of charges.
• The electric field at any point inside a conductor in electrostatic equilibriumis zero.
• Excess charges reside only on the surface of a conductor.
• When a conductor is in static equilibrium, only points on its surface can have a nonzero net charge.
• The electric field at the surface of the conductor is always perpendicular to the surface. For this reason, lightning rods have pointed edges

Shielding

• Electric field is zero inside a conductor
• Circuits and cables are shielded in Metallic enclosures to protect from electric fields
• When an external electric changes the free electrons in a metallic enclosures change to compensate for the new external electric field

Electric Fields of Charge Distributions

• The electric field due to a continuous charge distribution is calculated by integrating over the distribution.
• Volume charge density ρ is defined as ρ ≡ dQ/dV.
• Surface charge density σ is defined as σ ≡ dQ/dA.
• Linear charge density λ is defined as λ = dQ/dl.
• One has several equations for this including ΔΕ =ke Σ (Δqi / ri 2) r̂ E =k lim Σ (Δqi / ri 2) r̂ e Δαi → 0 dV =k f ( dq / r2) r̂

Examples using lambda

• Uniform positive charge per unit length λ dq = λdx dE = ke λdx/ x²
• Then one solves ∫dE =∫ ke λdx/ x²

Uniform Ring of Charge

• If x >> a then the Electric Field = kQ/x^2 dEₓ = kₑdq x/r^2
• Then one solves a line integral

Uniformly Charged Disk

• If R >> x then the Electric Field = sigma/2ε0 dq = 2πordr ∫
• dEx = dEx = (2πordr)* dEx = kₑdq x/(x^2 +r^2)
• Then one solves a line integral

Uniform Electric Fields

• A common way to create a uniform electric field is by using two plates charged with equal and opposite charges (creating a capacitor).
• With two plates: Electric Field between the plates: E = Q/ε0A Q
• ε0 =electric permittivity of free space and k = 1/4πE

Effects Of Electric Fields

• When under a uniform field electric field is F=qE =ma and α =eE/m
• and when at the line: y = -eE x²/ mv;² with the trajectory is a parabola

Cathode Ray Tubes

• Application: cathode ray tube contains plates for vertical and horizontal deflection