Plasma Physics Quiz

Physics 1: Electrostatic Field and Electric Current

• The course is Physics 1, taught by Dr. Kristina Bočkutė at KTU (Kaunas University of Technology)
• The course covers electrostatic fields, electric current, and related topics.

Minutes from the Last Lecture

• Ideal gas model: pV = nRT
• Thermodynamic processes: Isothermal, isochoric, isobaric, pV diagrams
• First Law of Thermodynamics: A generalization of energy conservation, including heat and mechanical work transfer.
• Second Law of Thermodynamics: It's impossible to convert all absorbed heat at a single temperature into mechanical work while returning the system to its original state. Heat cannot spontaneously flow from a cold body to a hot body.
• Third Law of Thermodynamics: A system's entropy approaches a constant value as its temperature approaches absolute zero.

1st Law of Thermodynamics

• Increase in internal energy in a gas process: equals the heat input plus the work done on the gas.

Heat Capacity

• The heat capacity at constant volume of an ideal gas depends on the number of molecules.

Pressure and Volume

• If the pressure of an ideal gas doubles during a process in which the heat given up by the gas equals the work done on the gas, then the volume is halved.

Outline

• Electric Charges: Coulomb's law, electrostatic fields, electric dipole, electric flux, Gauss's law, electric potential, capacitors, dielectrics, polarization, and summary.
• Electric Current: Drift velocity, current, current density, resistivity, resistance, electromotive force (emf), energy, and power.
• Direct-current circuits: Resistor connections (series and parallel), Kirchhoff's rules.
• Other Processes: A summary and introduction to next lecture's topics.

Electric Charge

• Historical introduction: The ancient Greeks discovered amber (elektron) attracted objects after rubbing.
• Two types of charge: Positive and negative
• Charges repelling each other: Like charges repel one another, while unlike charges attract.
• Structure of an Atom: Atoms consist of negatively charged electrons, positively charged protons, and uncharged neutrons.
• Mass and charge: The values are listed for electrons (me), protons (mp), and neutrons (mn)
• Atomic Number: The number of protons or electrons in a neutral atom.
• Ionization: Removing or adding electrons creates positive or negative ions.
• Principle of charge conservation: In any closed system the algebraic sum of all electric charges remains constant.
• Quantization of charge: All observable charges are always integral multiples of a fundamental electric charge e.
• Coulomb's law: The magnitude of electric force between two point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
• The proportionality constant k is 8.988 × 10^9 N⋅m²/C2

Electric Charge: Materials

• Insulators: Materials in which electric charges remain immobile
• Conductors: Materials through which electric charges can easily move
• Semiconductors: These lie between good conductors and good insulators.

Charging

• Insulators: Charged by rubbing
• Metals: Charged by contact
• Charges reside on the surface

Discharging

• Touching a charged object dissipates the charge.
• The Earth is a large conductor
• Grounding prevents build up of charges

Electric Field

• Electric force is long-range, no contact required
• Electric field : The alteration of space around a charged particle.
• A force is exerted on a charged particle when it enters the altered space.
• Electric field units: 1 newton per coulomb (1 N/C).
• Force on a point charge in an electric field: F = qE
• The electric field of a point charge always points away from a positive charge and toward a negative one.
• Electric field due to a point charge: F/q = E
• E = 1q/(4πεr^2); the unit vector from the point charge toward the measurement;

Superposition of Electric Fields

• The total electric field at a point is the vector sum of the fields due to individual charges, just as with forces.
• Linear, surface, and volume charge density are useful concepts

Electric Field Lines

• Electric field lines are imaginary lines used to visualize electric fields.
• Tangents to the lines at any point indicate the direction of the electric field vector.
• The spacing of lines gives a visual idea of the field strength.
• The lines never intersect.

Electric Dipoles

• An electric dipole is a pair of equal and opposite charges separated by a distance.
• The electric dipole moment is a vector quantity pointing from the negative to the positive charge.
• The magnitude of the dipole moment: is the product of the charge and separation.
• The torque on a dipole in a uniform electric field is given by M = pEsinθ
• The position ∅ = 0 is stable equilibrium, and ∅ = π is unstable.
• The potential energy of an electric dipole in a uniform electric field is given by U = –p⋅E

Electric Flux

• Electric flux describes the amount of an electric field passing through a surface.
• A positive flux indicates outward flux, and a negative flux indicates inward flux.
• The net electric flux through a closed surface is directly proportional to the net charge enclosed within the surface.

Calculating Electric Flux

• Gauss' Law: The net electric flux through a closed surface is directly proportional to the net charge inside that surface.

Gauss's Law

• Gauss's law relates the electric field to the total charge enclosed by a surface.
• A concept that allows calculating fields based on the distribution of charge.

Electrical Potential Energy

• The work done by the electric field: is equal to the change in potential energy.
• The work done by the field does not depend on the path.
• Work is negative if the movement is in the direction of the field
• Work is positive if the movement is in the opposite direction.
• Potential Energy: U = qV
• Potential Energy is determined relative to zero energy at infinity.
• Potential Energy due to a collection of point charges: U = (1/4πε) Σ(qiqj/rj)

Electrical Potential

• The potential energy per unit of charge (Potential is measured in Volts or Joules/Coulomb.)
• Potential due to a point charge : V=1q/(4πε0r)
• Potential of a collection of point charges: V=1/(4πε0) Σ(qi/ri)

Potential Gradient

• The potential gradient is the rate of change of potential per unit distance
• The electric field vector is negative potential gradient: E = –∇V

A Conductor in Electrostatic Equilibrium

• Excess charges reside on the surface.
• The electric field is zero inside the conductor.
• Any two points inside the conductor have the same potential.
• The electric field outside the conductor is perpendicular to the surface.

Sources of Electric Potential

• A battery creates a potential difference between two terminals, which depends on chemical reactions and transport of ions.
• The emf is the work per unit charge delivered by the battery.

Capacitors

• A capacitor stores electric charge and energy by holding opposite charges on two conductors separated by an insulator.
• The capacitance is the ratio of charge to the potential difference (C=Q/Vab)
• Capacitors have SI unit of farads (1F = 1C/V).
• A greater capacitance holds a greater potential difference given a certain charge.

Capacitance

• Parallel-plate capacitor capacitance: C=EA/d (in a vacuum or air; K is a dielectric constant).

Connection of Capacitors

• Series Combination: (1/Ceq) = (1/C₁)+(1/C₂)+(1/C₃)+...
• Parallel Combination: Ceq = C₁+C₂+C₃+...

Energy Stored in Capacitors

• U=1/2CV^2
• U=1/2Q^2/C

Dielectrics

• Dielectric materials are insulators inserted between capacitor plates.
• Increases capacitance over a vacuum
• Dielectric constant (K) : ratio of capacitance with dielectric to capacitance without.
• The dielectric constant is always greater than 1.

Induced Charges and Polarization

• Induced charges created due to polarization within the dielectric (equal but opposite charges on surfaces of polarized dielectric; net charge =0)
• Surface charge density due to polarization: σ₂ =(σ–σ₁), The electric field between the plates is related to the net surface charge density; Eo/E = K

Dielectric Breakdown

• Dielectric breakdown occurs when a dielectric material fails under strong electric field; the material eventually becomes a conductor.
• Dielectric strength is the maximum field with no breakdown.

Gauss's Law in Dielectrics

Ferroelectricity

• Ferroelectricity is a property of certain materials in which they possess spontaneous electric polarization that can be reversed.

Piezoelectricity

• Piezoelectric materials become charged when compressed.
• This effect is reversible meaning the crystal generates a voltage when compressed.
• This effect is also valid in reverse (A voltage causes a physical change/deformation of the material.)

Electric Discharge

• Is a flow of electric charge through a liquid, gas, or solid
• Townsend discharge occurs when free electrons gain energy.
• Glow discharge happens when the voltage is high enough to initiate Townsend discharge and some electrons are accelerated to the other end and generate light
• Arc discharge has high current
• Corona discharge has very small current

Plasma

• Plasma is a quasi-neutral gas of charged particles including ions and electrons.
• Plasma parameters are a criterion expressing the degree of plasma behavior; high Λ corresponds to approximate plasma behavior.
• Plasma frequency: a measure of the electron oscillations .

Next Lecture

• Magnetic fields in materials and a vacuum
• Electromagnetic Induction