Embedded Files
Outline of 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
Outline of 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)
Outline of 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
Outline of 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 s and –s (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 s and –s (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)
Outline of 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)
Outline of 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
Outline of 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)
Outline of 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)
Outline of 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
Outline of Lecture 10:
Full class devoted to example problems related to material covered in Lectures 1-8
Outline of 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
Outline of 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
Outline of 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)
Outline of 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)
Outline of 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)
Outline of 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)
Outline of 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)
Outline of 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
Outline of 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)
Outline of Lecture 19.5
Example problems involving Biot Savart Law
Outline of 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)
Outline of 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)
Outline of 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
Outline of 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 () (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
Outline of 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)
Outline of 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
Outline of 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
Outline of 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)
Outline of 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
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