Curricula »Peer Instruction Lecture Series

Peer Instruction Lecture Series

This lecture series for a calculus-based introductory physics course at the University of Pittsburgh by Professor Chandralekha Singh covers topics primarily in electricity and magnetism (the final lecture covers wave optics). Professor Singh is making these videos available to all students and instructors worldwide under the creative commons license. These lectures can also be helpful for high school students taking AP calculus-based electricity and magnetism.

These lectures make use of the peer instruction technique in which students talk to their peers and make sense of the material discussed. In all lectures EXCEPT lectures 1, 2, 7, 10, 18, 19.5, 20, 25, 25.5 and 27, students use "clickers" or a classroom response system to respond to "concept tests" [1] which are multiple-choice questions based upon the material covered in the lectures. Instructors can use these lectures to learn how peer instruction technique can be used in a large physics class.

As stated in Mazur's manual of peer instruction [1], the fundamental goal of implementing a peer instruction strategy in class is "to exploit student interaction during lectures and focus students' attention on underlying concepts". Peer interaction keeps students alert during the lectures because they know they must discuss the questions posed by the instructor with their peers, and the process helps them in the learning process and in organizing and extending their knowledge. Articulating one's opinion requires attention to logic and organization of thought processes. Instant feedback from students via clickers also provides a "reality check" to the instructors about the extent to which students have learned the concepts. This check can help instructors adjust the pace of the class appropriately. Moreover, there often is a mismatch between the instructor and the students' expectations of the level of understanding. Peer instruction helps convey the instructor's expectations to the students. An additional advantage of peer discussion is that it is embedded in a context that can help students retain and recreate the content by remembering the discussion. The peer instruction approach can be implemented without clickers, but clickers allow students to answer the questions anonymously and they also provide feedback to instructor which can be used to improve teaching (students can be awarded some additional incentive for answering clicker questions, e.g., 80% of the maximum point can be awarded to a student for each question for attempting it even if the answer is incorrect and 100% for answering it correctly).

  1. E. Mazur, Peer Instruction: A User's Manual, Upper Saddle River, NJ: Prentice Hall, 1997, pp. 7-10.

Please note each lecture video has details of what is discussed in its description section along with hyperlinks to places in the video where new topics start. Click on the hyperlink to start at a particular topic. Also, note that the topics covered in all of the lecture videos can be found by clicking here.

Jump to a Lecture: 1 · 2 · 3 · 4 · 5 · 6 · 7 · 8 · 9 · 10 · 11 · 12 · 13 · 14 · 15 · 16 · 17 · 18 · 19 · 20 · 21 · 22 · 23 · 24 · 25 · 26 · 27

Lectures 1 and 2

Lecture 1

  • Origin of electricity (Up to 16 m)
    • electrons and protons in atoms
  • Classification of materials based upon electrical properties (Starts at 16 m)
    • conductors
    • insulators
  • Charging an insulator by rubbing and charging a conductor by induction (starts at 21 m 30 s)
  • Coulomb's Law (starts at 55 m)
    • Electrostatic force between two point charges
  • Superposition principle (starts at 1 h 4 m 30 s)
    • Use of the superposition principle to find the net force on a point charge from other point charges

Lecture 2

  • Example problems including concept tests involving Coulomb's Law and the superposition principle (up to 40 m)
    • Collinear point charges (charges in a straight line)
    • Non-collinear point charges
  • Defining the concept of electric field (starts at 40 m)
  • Superposition principle (starts at 49 m 30 s)
    • Finding the electric field at a point due to two or more point charges using Coulomb's Law and the superposition principle
  • Electric field at a point due to a positive point charge or a negative point charge (both the magnitude and direction of the field) (starts at 55 m)
  • Example problems involving the electric field due to several point charges (starts at 1 h 21m 56 s)

Lectures 3 and 4

Lecture 3

  • Example problems including concept tests involving the electric field due to more than one point charge (up to 50 m)
  • Concept of electric field lines (Up to 1 h 16 m)
    • Electric field lines due to a positive point charge
    • Electric field lines due to a negative point charge
    • Electric field lines due to an electric dipole (two charges with equal magnitude but opposite sign separated by a distance)
  • Electric field of an electric dipole (Starts at 1 h 16 m)
    • Calculating the net electric field at a point on the axis of an electric dipole
    • Defining electric dipole moment
    • Calculating net electric field on the perpendicular bisector of an electric dipole

Lecture 4

  • Demonstrations related to electric field lines (First 6 m 30 s)
    • Electric field lines for a point charge
    • Electric field lines for an electric dipole
    • Electric field lines for two equal magnitude positive point charges
    • Electric field lines for a parallel plate capacitor
  • Example problems including concept tests involving electric forces and electric field due to several point charges (starts at 6 m 30 s)
  • Electric field due to continuous charge distributions (starts at 33 m)
    • Electric field due to a uniformly charged thin ring at a point on its axis
    • Electric field due to a disk with uniform charge at a point on its axis
      • Electric field at a point due to the disk with a uniform charge in the limit when the radius of the disk goes to infinity so that the disk can be thought of as an infinite sheet of charge
  • Electric field due to two thin parallel infinite sheets with uniform surface charge densities C3 and –C3 (starts at 1 h 5 m)
    • Electric field between the two infinitely large metal plates of a parallel plate capacitor where the inner plates have surface charge density C3 and –C3 (two infinite parallel metal plates with a uniform surface charge density of equal magnitude but opposite sign on the inner surface of each plate)
      • Note that here we are not interested in the electric field inside the conducting plates (which is always zero in equilibrium)
  • Example problems involving motion of a positive charge launched with an initial velocity perpendicular to the uniform electric field within a parallel plate capacitor (e.g., calculation of time for which the charge is in the uniform electric field, the distance traveled perpendicular to the field for the time the particle is in the field etc.) (starts at 1 h 19 m)
    • Analogy between the charged particle in a uniform electric field and the motion of a projectile in a uniform gravitational field near the earth's surface
  • Torque on an electric dipole in a uniform external electric field (starts at 1 h 37 m)

Lectures 5 and 6

Lecture 5

  • Example problems including concept tests related to electric field and electric force (First 6 m 50 s)
  • Torque on an electric dipole in a uniform external electric field (starts at 6 m 50 s)
  • Potential energy of an electric dipole in an external electric field (starts at 22 m)
  • Motivation for why Gauss's Law (instead of Coulomb's Law) may be more suited for calculating electric field when the charge distribution has an extremely high level of symmetry (starts at 43 m)
  • Definition of electric flux (starts at 50 m)
  • Gauss's law (starts at 1 h 10 m)
    • Relation between electric flux through a closed surface and charge enclosed by the surface
  • Gauss's Law and Coulomb's Law are equivalent (starts at 1 h 26 m)
  • Finding the electric field due to a uniform spherical shell using Gauss's law by invoking symmetry (starts at 1 h 36 m)

Lecture 6

  • Example problems including concept tests related to electric field, electric flux and Gauss's Law (First 16 m 30 s)
  • Invoking symmetry to find the electric field due to a spherically symmetric charge distribution (starts at 16 m 30 s)
    • Use of Gauss's Law to find the electric field at a point due to a uniform spherical shell (up to 43 m)
    • Use of Gauss's Law to find the electric field at a point due to a uniform spherical volume distribution of charge (starts at 43 m)
  • Invoking symmetry to find the electric field due to a cylindrically symmetric charge distribution (starts at 1 h 6 m)
    • Use of Gauss's Law to find the electric field at a point due to a uniformly charged infinitely long line of charge (starts at 1 h 6 m)
    • Use of Gauss's Law to find the electric field at a point due to a uniformly charged infinitely long cylinder (starts at 1 h 25 m)
  • Invoking symmetry to find the electric field due to a charge distribution having planar symmetry (starts at 1 h 36 m)
    • Use of Gauss's Law to find the electric field due to an infinite sheet of uniform charge

Lectures 7 and 8

Lecture 7

  • Example problem related to electric field at a point in a spherical cavity in a uniform spherical volume distribution of charge (the cavity is not concentric with the sphere with the volume charge distribution)
  • Example problem related to electric flux through a closed cylinder in a uniform electric field (Starts at 25 m)
  • Invoking symmetry to find the electric field due to a charge distribution with planar symmetry (Starts at 37 m)
    • Gauss's law to find the electric field due to an infinite sheet of uniform charge
  • Conductors and electrical shielding (Starts at 51 m)
    • Electric field inside a conductor must be zero in equilibrium
  • All excess charges on the conductor must reside on the outer surface of the conductor for the electric field inside the conductor to be zero
    • Proof using Gauss's Law
  • Problems involving equilibrium configuration of charges on a conductor
    • Excess charges placed on a conductor must always be on the outer surface of the conductor
    • Induced charges on the conductor due to charges outside the conductor (close to the conductor) must be on the outer surface to shield the conductor and make the net electric field zero everywhere within the conducting material
    • Charges placed in the cavity of a hollow conductor can induce charges BOTH on inner and outer surfaces of the conductor (1 h 31 m)

Lecture 8

  • Example problems including concept tests related to electrostatics including those involving conductors (First 34 m)
  • Problems involving the equilibrium configuration of charges on hollow conductors (starts at 34 m)
    • With excess charges on the surface of the conductor
    • Charges in the cavity within the conductor
    • Charges outside the conductor which may induce charges on the surface of the conductor
  • Experiments involving electroscopes (starts at 44 m 30 s)
    • Electric field inside a conductor is zero in equilibrium
    • All excess charges on the conductor lie on the outer surface in equilibrium (no excess charge on the inner surface of the conductor even if initially we may have placed excess charges on the inner surface by touching the inner surface of the conductor with another charged object)
  • A spherical conductor placed in a uniform electric field (starts at 50 m)
    • Charge distribution and electric field when equilibrium is established
      • Distorted electric field lines (electric field is no longer uniform) due to induced charges on the surface of the conductor
      • Electric field inside the conductor is zero in equilibrium as always
      • Electric field lines right outside of the conductor will terminate perpendicular to the surface of the conductor everywhere; otherwise induced charges on the surface of the conductor will feel an electric force
  • Electrostatic potential energy (starts at 56 m)
    • Motivation for a new concept
    • Analogy between problems involving electrostatic potential energy and those learned earlier involving gravitational potential energy
    • Relation between work done by the electrostatic force and change in electrostatic potential energy
    • Example problems
  • Electric Potential (starts at 1 h 18 m)
    • Relation between potential and potential energy
    • A positive charge accelerates from a region with a higher electric potential to a region with a lower electric potential and a negative charge accelerates from a region with a lower electric potential to a region with a higher electric potential
  • Example problem involving conservation of mechanical energy in which mechanical energy includes kinetic energy and electrical potential energy (changes in gravitational potential energy are negligible) (starts at 1 h 33 m)

Lectures 9 and 10

Lecture 9

  • Half of this lecture is devoted to example problems including concept tests related to material covered in Lectures 1-8 (First 46 m)
  • Electric potential and electric potential energy (starts at 46 m)
  • Relation between electric field and electric potential (starts at 51 m 30 s)
  • Derivation of potential due to a point charge (starts at 56 m)
    • Plotting potential due to a point charge
  • Potential due to several point charges (1 h 8 m 25 s)
  • Equipotential surface (1 h 21 m 30 s)
    • Work done by the electric force is zero when a test charge is moved from one point to another on an equipotential surface
    • Electric field everywhere is perpendicular to equipotential surface
    • Equipotential surfaces due to a point charge
    • Equipotential surfaces due to a parallel plate capacitor
    • Equipotential surfaces due to an electric dipole

Lecture 10

  • Full class devoted to example problems related to material covered in Lectures 1-8

Lectures 11 and 12

Lecture 11

  • Example problems including concept tests (First 31 m 20 s)
    • Relation between the potential difference and electric field
    • Calculating potential difference from information about the electric field
  • Equipotential surface (starts at 31 m 20 s)
  • If the electric field everywhere inside a conductor is zero in equilibrium, then (starts at 40 m)
    • the body of the conductor must be an equipotential volume
    • an empty cavity inside a conductor is also an equipotential volume
  • Any region where the electric field is zero everywhere must be an equipotential surface or volume
  • Potential due to a uniform sphere of charge (starts at 47 m 30 s)
  • Potential due to an infinite line of charge (starts at 59 m 40 s)
    • Example problem involving conservation of mechanical energy with a test charge moving from one point to another close to an infinite uniform line of charge (starts at 1 h 8 m 30 s)
  • Finding the electric field from the information about the electric potential (starts at 1 h 18 m)
    • Examples showing how to find the electric field components from the functional form of the electric potential (i.e., when electric potential is given as a function of x, y and z)
    • Example problem
  • Potential energy of a system of charges (1 h 29 m)
    • Example problem
  • Methods for calculating the work done by the electric force in moving a test charge from one point to another (1 h 36 m)
    • In terms of the electric field
    • In terms of the change in the potential energy
    • Example problem involving the work done by the electric force (vs. work done by an external agency) in moving a test charge from one point to another between the plates of a parallel plate capacitor

Lecture 12

  • Example problems including concept tests (First 9 m 30 s)
  • Capacitors and capacitance of a capacitor (starts at 9 m 30 s)
  • Applications of capacitors (starts at 14 m)
  • Charging a capacitor (starts at 16 m 30 s)
  • Defining capacitance of a capacitor (starts at 26 m 30 s)
  • Capacitance of a parallel plate capacitor (starts at 38 m 51 s)
  • Capacitance of a spherical capacitor (starts at 47 m)
  • Capacitance of a cylindrical capacitor (starts at 55 m 40 s)
  • Capacitors in series and parallel (starts at 1h 1 m)
    • Network of capacitors composed of series and parallel combinations
    • Example problems related to network composed of capacitors in series and parallel combinations

Lectures 13 and 14

Lecture 13

  • Example problems including concept tests (First 20 m 40 s)
  • Example problems related to network composed of capacitors in series and parallel combinations (starts at 20 m 40 s)
    • Equivalent capacitance
    • Determining charges on various capacitors in a circuit from given information
  • Electrical energy stored between the plates of a capacitor ignoring edge effects (starts at 40 m)
  • Electrical energy density (energy/volume) associated with an electric field between the plates of a capacitor (51 m 10 s)
  • Dielectric (instead of vacuum or air) between the plates of a capacitor (1 h 1 m 10 s)
    • Effect on capacitance, electric field and potential difference between the plates
    • Microscopic view of dielectrics
  • Experiments with Van de Graaff generator (starts at 1 h 29 m 30 s)
    • Very high potential on the dome with respect to ground
      • Very large amount of charges accumulates on the outer surface of the dome
      • Pom-pom placed on the dome picks up the same type of charge as the dome and spreads out since like charges repel
    • All excess charges on the outer surface of the dome
    • Volta's hail storm experiment (note: when one plate of the parallel plate capacitor is connected to the Van de Graaff generator via a wire, that plate acquires a large amount of the same type of charge as the charge on the dome of the Van de Graaff. The other plate of the capacitor which is grounded acquires the opposite charge. The Styrofoam pieces can also acquire the same type of charge as the charge on the capacitor plate they are sitting on (which leads to repulsion between Styrofoam and that plate). Hail storm will occur if the charges that the Styrofoam pieces pick up from the plate lead to a repulsion large enough so that the Styrofoam pieces go to the other plate, then pick up charges there and get repelled from that plate and so on and so forth)
    • Demonstration of electrical shielding inside a conductor
      • Electric field inside a conductor is zero in equilibrium
    • Lighting a fluorescent tube light by providing high potential difference between the two ends of the fluorescent tube light (by placing one end close to the Van de Graaff generator)

Lecture 14

  • Example problems including concept tests (First 19 m)
    • The last problem is related to the change in capacitance when a dielectric is introduced at fixed potential difference between the plates of a capacitor vs. when the charge on the plates is kept fixed
  • Charges in motion (starts at 19 m)
    • Current
    • Current density (starts at 26 m)
    • Drift speed (starts at 33 m)
    • Relation between current density and drift velocity (starts at 39 m 50 s)
    • Resistivity and resistance (starts at 54 m)
    • Ohm's law (starts at 58 m)
      • relation between electric field and current density (for the case where the resistivity is independent of the electric field)
      • relation between voltage and current (for the case where the resistance is independent of the electric field)
    • Temperature dependence of resistivity (starts at 1 h 9 m 45 s)
    • Relation between resistivity and mean free time (the average time between collision) (1h 23 m 30 s)
    • Power output of a battery (starts at 1 h 36 m)
    • Power dissipated in the form of heat in a resistor (starts at 1 h 42 m 10 s)

Lectures 15 and 16

Lecture 15

  • Example problems including concept tests (up to 9 m)
  • emf of a battery (starts at 9 m)
  • Kirchhoff's rules (starts at 13 m 30 s)
    • Current rule
    • Voltage rule
  • Application of Kirchhoff's rules (starts at 29 m 15 s)
  • Equivalent resistance of resistors in series, parallel or networks composed of series and parallel combinations (series starts at 34 m 30 s and parallel starts at 44 m 50 s)
  • Problems involving light bulbs in series and parallel assuming they are Ohmic resistors, including power dissipation in each light bulb (brightness of the light bulbs) (1 h 14 m 30 s)

Lecture 16

  • Example problems including concept tests (First 21 m)
  • Definition of the non-SI unit of energy "electron volt" (starts at 21 m)
  • Ammeter and Voltmeter (27 m 40 s)
    • What they measure
    • Their internal resistance
    • How they are connected in circuits
  • Battery with an internal resistance (39 m)
    • Power output of a battery
  • Resistive circuits with a battery with an internal resistance (40 m)
  • Simple capacitive-resistive circuit where the capacitor and resistor are in series (starts at 44 m)
    • Charging a capacitor
    • RC time constant
    • Discharging a capacitor (Starts at 1 h 13 m 20 s)
  • Motivating the next topic: magnetism (1 h 30 m)

Lectures 17 and 18

Lecture 17

  • Most of the lecture is focused on example problems including concept tests from lecture 9 and lecture 11 through lecture 14 (up to 1 h 16 m 20 s)
  • The rest of the lecture is focused on solving example problems involving circuits, e.g., involving light bulbs in series and parallel (1 h 16 m 20 s)
  • Origin of magnetism in bar magnets (1 h 34 m 44 m)

Lecture 18

  • The first 24 m are devoted to example problems from material covered in lecture 9 and lecture 11 through lecture 14 (up to 23 m 20 s)
  • Magnetism (Starts at 23 m 20 s)
    • Magnetic material, magnetism of a bar magnet vs. magnetism due to a current carrying wire
    • Magnetic field lines of a bar magnet
    • Comparison of the magnetic field lines of a bar magnet (magnetic dipole) and electric field lines of an electric dipole
      • Magnetic field lines always form closed loops since there are no isolated north or south poles
    • Magnetism of earth

Lectures 19 and 19.5

Lecture 19

  • Example problems including concept tests (First 3 m 35 s)
  • Magnetism (Starts at 3 m 35 s)
  • Convention for how to represent a vector pointing into the paper or blackboard and a vector pointing out of the paper or blackboard (Starts at 13 m)
  • Magnetic force on a charged particle in an external magnetic field (16 m 30 s)
    • Right hand rule for the direction of force
  • Velocity selector: Charged particle in an electric and magnetic field which are perpendicular to each other and to the direction of the velocity (starts at 35 m 20 s)
  • Trajectory of a charged particle in a uniform external magnetic field when the particle is initially launched perpendicular to magnetic field (starts 47 m 30 s)
    • Uniform circular motion
    • Relation between the radius of the circular trajectory, speed and magnetic field
    • Relation between frequency, angular frequency, period (time for one full circle) and magnetic field
  • Cyclotrons and synchrotrons (1 h 9 m 25 s)
  • Mass spectrometer ( 1h 20 m)
  • Magnetic force on a very long straight current carrying wire in an external magnetic field (Starts at 1 h 23 m 40s)
    • Right hand rule for the direction of magnetic force on a current carrying wire
  • Torque on a current carrying coil in an external magnetic field (Starts at 1 h 30 m 40 s)

Lecture 19.5

  • Example problems involving Biot Savart Law

Lectures 20 and 21

Lecture 20

  • The beginning of the lecture dealing with concept tests and quantitative treatment of torque on a current loop in a magnetic field could not be recorded due to technical issues
  • Biot Savart Law (up to 4 m)
    • Magnetic field produced by an infinitesimal current element
  • Ampere's Law (starts at 4 m)
    • Magnetic field produced by a long straight current carrying wire at a distance r from the wire
    • Right hand rule for finding the magnetic field due to current
  • Example problem involving the net magnetic field due to two infinitely long straight current carrying wires using the superposition principle (37 m 10 s)

Lecture 21

  • Example problems including concept tests (First 12 m)
  • Magnetic Force between two straight infinitely long current carrying wires (starts at 12 m)
    • Wires carrying current in same direction attract
    • Wires carrying current in opposite directions repel
  • Magnetic field due to an infinitely long solenoid (Starts at 44 m 20 s)
  • Magnetic field due to a tightly wound toroid (starts at 1 h 7 m 40 s)
  • Faraday's Law of electromagnetic induction (starts at 1 h 23 m 10 s)
  • Magnetic flux (1 h 29 m 20 s)

Lectures 22 and 23

Lecture 22

  • Example problems including concept tests (First 11 m)
  • Faraday's Law (starts at 11 m)
  • Lenz's Law (starts at 16 m 20 s)
    • Direction of induced current when the magnetic flux through a coil changes
    • Example problems
  • Applications of Faraday's Law (starts at 32 m 50 s)
    • Transformers
    • Magnetically levitated trains
  • Analogy between a bar magnet and a current carrying loop (37 m)
  • Eddy currents (42 m)
    • A breaking effect: Dissipative eddy currents in a metal tube will slow down a bar magnet dropped from a vertically suspended metal tube (same principle as magnetically levitated trains)
  • Motional emf (starts at 1 h 6 m)
    • Very nice example that helps make sense of Lenz's Law
      • Lenz's Law is consistent with the conservation of energy

Lecture 23

  • Example problems including concept tests involving Faraday's Law and Lenz's Law (First 16 m)
  • Example problem involving the magnetic force on a charged particle in which the magnetic field and velocity vectors are in component form (i ^,j ^,k ^) (starts at 16 m)
  • Example problem involving motional emf (starts at 33 m 30 s)
  • Induced electric field (starts at 47 m 50 s)
    • Writing Faraday's Law in terms of induced electric field
  • How induced emf is different from the emf of a battery (starts at 58 m)
    • Induced electric field in Faraday's Law is different from electric field encountered in electrostatics
  • Inductor (starts at 1 h 0 m 25 s)
    • Self-inductance (or simply inductance) of an inductor
    • Inductance of an inductor only depends on the geometric and intrinsic properties of the inductor for linear materials
      • Inductance does not depend on current or magnetic flux
      • Analogy with resistance of an Ohmic resistor and capacitance of a capacitor which also depend on geometry and intrinsic properties only such as resistivity (for resistance) or dielectric constant (for capacitance)
  • Inductance of an infinitely long solenoid (1 h 6 m)
  • Circuits involving inductors and resistors in series (LR circuits) (Starts 1 h 15 m)
    • Motivation and qualitative analysis of a simple LR circuit
    • Current as a function of time with a battery in the circuit, after the switch is closed

Lectures 24 and 25

Lecture 24

  • Example problems including concept tests (First 9 m 30 s)
  • LR circuits (starts at 9 m 30 s)
    • Circuits involving inductors and resistors in series
    • Current as a function of time
    • Time constant of an LR circuit
    • When there is a battery in the circuit and the switch is closed
    • When the switch is opened so that battery is not in the circuit and the closed circuit only has the inductor and resistor
  • Magnetic energy stored in an inductor (starts at 30 m 9 s)
  • Magnetic energy density (energy/volume) associated with a magnetic field stored in an inductor (starts at 37 m)
  • Mutual inductance (starts at 46 m)
  • Ideal Transformer (starts at 55 m)
    • Step up and step down transformers
    • Voltage in the primary (input) and the secondary (output) coils
    • Current in the primary and the secondary coils
  • Circuits involving inductors and capacitors (starts at 1 h 24 m 35 s)
    • An ideal LC circuit (without loss of energy)
    • Conceptual analysis of why charge on capacitor plates and current in the circuit will oscillate as a function of time (sinusoidal function of time)
    • Conceptual analysis of why the energy stored in the electric field of the capacitor and the energy stored in the magnetic field of the inductor will be periodic in time
    • Example problem showing how energy conservation can be used to find the maximum current in an LC circuit given L, C and the voltage of the battery that was used to charge the capacitor before it was connected to the LC circuit (starts at 1 h 40 m)

Lecture 25

  • Many example problems on magnetism up to Faraday's and Lenz's Laws (First 40 m 30 s)
  • Experiments related to transformer with different windings of the input (primary) and output (secondary) coils (starts at 40 m 30 s)
  • LC oscillation (Starts at 46 m 25 s)
    • Electrical mechanical analogy (comparison of an LC system with a mass-spring system)
    • Quantitative analysis of an LC circuit
    • Charge on a capacitor and current in the circuit as a function of time
    • Energy stored in the electric field between the plates of capacitor and energy stored in the magnetic field of inductor as a function of time
  • Example problems involving LC circuits (1 h 23 m)
  • Damped oscillations in an RLC circuit (1 h 37 m 30 s)
    • Both quantitative and conceptual analysis of a damped RLC circuit

Lectures 25.5 and 26

Lecture 25.5

  • Maxwell's Law of induction
    • This lecture was not recorded with other lectures because it was at the end of the class on the same day an exam was given and the recording device was not set

Lecture 26

  • Example problems including concept tests involving Maxwell's Law of induction (Maxwell's generalization of Ampere's Law), displacement current, induced magnetic field and energy density stored in the magnetic field (First 20 m)
  • Example (quantitative) problem involving Maxwell's Law of Induction, displacement current and induced magnetic field (starts at 20 m)
  • All four Maxwell's equations (in free space) (starts at 34 m)
    • Gauss's Law of electricity
    • Gauss's Law of magnetism
    • Faraday's Law of electromagnetic induction
    • Maxwell-Ampere Law: combining induced magnetic field due to changing electric field (Maxwell's law of induction) and magnetic field produced by current carrying wire (Ampere's Law)
  • Nature of Electromagnetic or EM waves (starts at 39 m 15 s)
    • Electromagnetic waves are able to travel through vacuum (no need for a medium for propagation unlike sound waves that require a medium)
    • Relation between the direction of electric field, direction of magnetic field and direction of propagation of an EM wave in vacuum
    • Spectrum of electromagnetic waves
    • Relation between speed, frequency and wavelength
    • Relation between the speed of light in vacuum and permeability constant and permittivity constant of free space
    • Relation between the magnitude of electric field and magnetic field (at any point in time) in an EM wave
  • Energy carried by an electromagnetic wave (58 m)
    • Poynting vector of EM waves
    • Intensity of EM waves
    • Energy density (energy per unit volume) in the electric field of an EM wave
    • Energy density (energy per unit volume) in the magnetic field of an EM wave
    • Energy density in the electric field and magnetic field of an EM wave in vacuum are the same
  • Polarization of light (1 h 22 m)
    • Any transverse wave, e.g., wave on a string, displays polarization phenomenon
    • In vacuum, light is a transverse wave with electric field and magnetic field of light perpendicular to the direction of propagation of wave
    • Intensity of unpolarized light reduced by a factor of two after passing through an ideal polarizer
    • Intensity of polarized light after passing through a polarizer
      • Malus's law
  • Reflection of light (starts at 1 h 35 m 30 s)

Lecture 27

Lecture 27

  • Refraction of light (First 30 m)
    • Speed of light changes when light goes from one medium to another
    • Frequency remains the same but wavelength changes when light goes from one medium to another
    • Refractive index of a medium
    • Snell's Law of refraction
    • Total internal reflection
    • Actual depth vs. apparent depth due to refraction of light
  • Interference of light (starts at 30 m 15 s)
    • Completely constructive and completely destructive interference (33 m 47 s)
    • Coherent sources (37 m 30 s)
    • Condition for observing completely constructive and completely destructive interference (starts at 44 m 30 s)
    • Young's double slit experiment (starts at 45 m 10 s)
      • Condition for observing bright and dark fringes on a far off screen
      • Example problem
    • Single slit diffraction (narrow slit) (starts at 57 m 45 s)
      • Condition for observing dark spots in the diffraction pattern
    • Diffraction through circular aperture (starts at 1 h 13 m)
      • Rayleigh criteria for resolving two objects through a narrow circular aperture
      • Example problems