Ace Electricity & Magnetism in 11 Hrs (The Complete Course)

Explore the electrostatic force by examining how positive and negative charges interact, with attraction and repulsion, and quantify charge using protons, electrons, coulombs, and the electron's charge.

Explore how charge is quantized in integer multiples of e and conserved in isolated systems, then distinguish insulators from conductors, noting rubbing, direct contact, and surface charge redistribution.

Charge a conductor by induction through grounding, showing electron transfer that yields a net positive charge, and explore polarization by induction in conductors and insulators to attract neutral objects.

Explore Coulomb's law, detailing the electrostatic force between two point charges with magnitude 8.99e9 q1 q2 over r^2, where unlike charges attract and like charges repel.

Apply Coulomb's law to the Bohr hydrogen model to find electron speed in a circular orbit, 2.8×10^6 m/s, with the electric force as the centripetal force and gravity negligible.

Explore the superposition of electric forces by summing vector forces from multiple charges to find the net force on a charge, using Coulomb's law in three examples.

Revisit polarization by induction in insulators; external charge near an atom creates charge separation and a polarized atom, yielding a net force toward the external charge, per Coulomb's law.

Explore the electric field concept, distinguishing Newtonian and field models, defining field strength and direction, how source and test charges interact, and how field is independent of test charge.

Explore how a point charge generates a field via Coulomb's law and constant, deriving E = k Q / r^2 r-hat and noting the direction depends on the source charge.

Explore how multiple source charges produce a net electric field by vector sum of individual fields, using the superposition principle and E equals k q over r squared.

Learn how electric field lines visualize field direction and magnitude, with density indicating strength, showing lines from positive to negative charges and uniform fields like a parallel plate capacitor.

Analyze a charged particle's motion in a uniform downward electric field between parallel plates, solving for field strength, exit speed, and proton displacement compared to the electron using kinematic equations.

Learn how a charged body's electric field arises from distributed charge by integrating infinitesimal elements dq. Apply the integral dq over r squared in the direction r-hat via superposition.

Derive the electric field from line charge distributions using line charge density and dq = lambda dl, then apply symmetry to find the net field.

Compute the electric field at point p due to a finite line charge of length L with constant density lambda, above the left end; resolve Ex and Ey by integration.

Compute the net electric field at point P for a uniformly charged ring by symmetry and integration, yielding the x-component E_x = k Q x /(x^2+R^2)^(3/2).

Compute the electric field from a charged area by integrating surface charge density over elements. For a uniform disk, rings yield E along x, approaching E = sigma/(2 epsilon naught).

Learn to find the electric field from volume charge using rho and small volume elements. Replace Dq with rho D tau and take the integral to obtain the net field.

Gauss's law and electric flux, defined as E·A for uniform fields and as a surface integral of E·dA, and learn how orientation and closed surfaces influence flux.

Apply Gauss's law to compute the net electric flux through any closed surface using the total charge enclosed, via the relation flux equals the enclosed charge divided by epsilon naught.

Explore Gauss's law through symmetry: planar, cylindrical, and spherical cases, deriving electric fields for a line of charge, infinite plane, two opposite planes, and a solid sphere.

Describe four properties of conductors in electrostatic equilibrium: zero interior electric field, surface-only excess charge, perpendicular surface field, and E = sigma/epsilon naught relation, including hollow conductors with induced charges.

Apply Gauss's law to a conducting spherical shell with center charge Q and net -3Q; derive the electric field for r<a, a<r<b, and r>b, noting inner and outer surface charges.

Learn how a hollow conductor with zero net charge forms a Faraday cage that makes the electric field vanish inside the hollow region, with everyday examples like microwaves and elevators.

Review of work covers line integrals of force along a path, the work–energy relation for conservative forces like gravity, and energy conservation between kinetic and potential energy.

The lecture links electric potential energy to gravitational energy, showing how conservative work equals negative potential energy change, and how charges move with or against the field.

Analyze electric potential energy through two examples: a moving electron in a uniform field and protons/electrons between a charged parallel plate capacitor, applying work, conservative forces, and energy conservation.

Compute the potential energy of the system of two point charges using Coulomb's constant k, Q1 Q2 divided by R, with zero at infinity and sign determined by the charges.

Explore potential energy in point-charge systems, compute external work to move a charge, and apply conservation of mechanical energy to find a final speed for four charges at square corners.

Define electric potential as the potential energy per unit test charge. Apply V = kQ/r with zero at infinity; outside a uniformly charged sphere it behaves as a point charge.

Show how electric potential depends on source charges and uses superposition for multiple sources. Demonstrate integrating dV = (1/4πε0) dq / r for line, ring, and disk charge distributions.

Revisit electric potential, showing that work by the electric force equals negative q ΔV, U = qV, and that moving to lower potential yields positive work and introduces electron volt.

Explore how conservation of energy governs motion when potential energy is replaced by Q times electric potential, showing how positive charges slow at higher potential and negative charges speed up.

Derive the potential difference from a known uniform electric field by relating the work of electric force to changes in potential energy, using delta V = - E · ds.

Explain how Ex = -∂V/∂x, Ey = -∂V/∂y, Ez = -∂V/∂z, and Delta V = -∫ E·ds, with notes that constant or zero potential along x yields Ex = 0.

Investigate equipotential surfaces and their perpendicular relationship to electric field lines, using dv equals zero and contour visuals to illustrate constant potentials around charges and plates.

Conductor in electrostatic equilibrium features a field perpendicular to the surface, a constant surface potential with zero interior field, and equipotential; outside, a spherical charge behaves like a point charge.

Explore capacitance and dielectrics: how two conductors separated by an insulator in a parallel-plate capacitor store charge, the C = Q/ΔV relation, and how geometry and dielectric affect stored charge.

Explore how capacitors store charge and connect in parallel or series, deriving the equivalent capacitance: Ceq = C1 + C2 in parallel, and 1/Ceq = 1/C1 + 1/C2 in series.

Analyze a circuit with three capacitors, two in parallel and one in series, powered by 12 v battery. Compute the equivalent capacitance and the charges and voltages on each capacitor.

Derive the work to charge a capacitor and the energy stored as Q^2/(2C) or 1/2 C (ΔV)^2, and state the energy density is ε0/2 |E|^2.

Charge an 8 µF capacitor to 120 V; connecting to a 4 µF capacitor yields final 80 V with redistributed charge, and energy drops to 0.039 J due to heat.

Insert a dielectric between the plates of a parallel-plate capacitor to increase capacitance, as polarization reduces the net field and yields C = κ C0, with or without a battery.

Explore dielectrics in capacitors, showing how water (kappa 80) raises capacitance from 5 nF to 400 nF and voltage from 160 V to 20 V, with energy lost as heat.

Explore current and resistance by defining current as the net flow of charge through a surface. Conduction electrons act as charge carriers, moving under a potential difference and electric field.

Explore drift speed, current density, and conductivity, relate them to electron density and cross-section, and illustrate with a copper wire example.

Learn how resistance arises from material resistivity, length, and area, derive ohm's law ΔV = IR, and compare conductors, insulators, and ideal cases using a water flow analogy.

Compare current, current density, drift speed, and resistance in two wire segments of equal length but different diameters, then solve a copper wire example for electric field and resistance.

Learn how dc current flows through rc circuits with resistors and capacitors, driven by emf from a battery, and understand ideal emf sources, potential difference, and emf units.

Master Kirchhoff's laws—the junction rule and loop rule—for current and energy conservation in circuits, including EMF sign conventions and resistor voltage calculations.

Explore energy and power in a DC circuit with a battery and resistor, showing how EMF sustains a constant voltage and heat results from P = IV.

Explore resistors in series and parallel, applying Kirchhoff's loop rule and Ohm's law to define equivalent resistances. Discuss real batteries with internal resistance and currents along parallel paths.

Demonstrate resistors in series and parallel by measuring current and voltage with emf and a voltmeter, compute internal resistance, and apply Kirchhoff’s loop rule to find equivalent resistances and currents.

Apply Kirchhoff's junction and loop rules to direct current circuits, analyze series and parallel resistors, define currents and voltages, and solve for unknowns, yielding equivalent resistance and potential differences.

Explore RC circuits with a resistor and capacitor, analyze charging dynamics, derive time dependent current and charge using loop rule and differential equations, and understand the time constant RC.

This lecture explains the discharge of an rc circuit after removing the battery, deriving q(t) = q0 e^{-t/rc} and i(t) = (q0/rc) e^{-t/rc}, plus charging and square-wave input.

Analyze an RC circuit to compute the capacitor voltage (6 V) and the discharge time (8.3 microseconds) using a 3.6 ohm equivalent resistance and a 1 microfarad capacitor.

Explore the magnetic field and magnetic force, including north and south poles, attraction and repulsion, Earth's field, compass alignment, magnetic field lines, and tesla magnitudes.

Explore how a moving charge and a steady current produce magnetic fields using the cross product and the right-hand rule, via v × r̂ / r² and current integration.

Derives the magnetic field magnitude from a straight current-carrying wire at distance a using the Biot–Savart law, with theta1 and theta2, infinite-wire limit, and circular field via the right-hand rule.

Apply the Biot-Savart law to current-carrying wires, showing circular segments alone produce the field at the origin and deriving the loop on-axis field; preview solenoids.

Explore how a circular current loop forms a magnetic dipole with a bar magnet field, and use the right-hand rule to define the dipole moment as current times loop area.

Derive the solenoid’s magnetic field by superposing loop fields with Bolsover’s law; for an ideal infinitely long solenoid, the field inside is mu0 n I and outside is zero.

Examine how atomic magnetism arises from electrons orbiting the nucleus and spin. Ferromagnetic materials such as nickel, iron, and cobalt show domain alignment under external fields, producing persistent magnetization.

Discover how magnetic fields push moving charges using F = q v × B, magnitude q v B sin θ, and the right-hand rule, noting magnetic force does no work.

Compute the net force on a charge in perpendicular electric and magnetic fields using F equals q(v cross B) plus qE; both forces point along +z, totaling about 0.073 N.

Discover how magnetic fields drive charged particles into circular motion when perpendicular to the field, and into helical paths when a field component remains, with Earth's aurora as a showcase.

Show how a velocity selector sets particle speed with electric and magnetic fields, enabling a mass spectrometer; relate orbit radius to mass and charge using uranium isotopes 235U and 238U.

Learn how magnetic fields act on current-carrying wires, determine the force with the right-hand rule, and see how parallel wires attract or repel.

examine two wires connected by springs to find the current for a 5–6 cm stretch, applying the right-hand rule, magnetic field, and Hooke’s law.

Learn to compute magnetic force on a non straight current-carrying wire by integrating over infinitesimal segments; in a uniform field, a closed loop has zero net force.

Show how a current loop in a uniform magnetic field experiences zero net force but nonzero torque; derive torque as I A cross B and μ = I A.

Apply the right-hand rule to magnetic torques on a uniform-field rectangular loop and rank loops A, B, and C; compute a circular coil’s magnetic moment and torque.

Explain how the magnetic force on a current loop powers an electric motor, with a coil and a commutator reversing current every 180 degrees, enabling rotation in everyday devices.

Define magnetic flux as surface integral of B dot dA and dependence; note zero flux for closed surfaces, shown by a loop near a current-carrying wire with μ0 I/(2π) ln((C+A)/C).

Faraday's law shows a changing magnetic flux induces an EMF and current in a circuit. The EMF equals the negative time derivative of flux, with direction set by Lenz's law.

Apply Faraday's law to differentiate the time-dependent magnetic flux through a loop inside a uniform field solenoid. Determine the induced current via Ohm's law from the resulting emf.

Move a conductor in a uniform magnetic field to generate motional emf, causing charge separation, an electric field, and a current that illustrates energy transfer from mechanical to electrical energy.

Apply Faraday's law and Lenz's law to determine the direction of induced currents opposing magnetic flux changes, using the right-hand rule and flux scenarios.

Revisit motional emf and Lenz's law for a rectangular loop near a current-carrying wire, analyzing how loop motion alters magnetic flux and induces emf and current via Faraday's law.

Eddy currents are circular currents that oppose changing magnetic flux when a magnet moves near metal, producing clockwise or counterclockwise fields, as shown by the pipe demo and metal detectors.

Explore how alternating current generators convert mechanical energy from natural sources into electrical energy, using Faraday's law to derive sinusoidal induced emfs and their out-of-phase relation with magnetic flux.