📘 What is electric charge really doing?

What you’ll learn

1. The Nature of Electric ChargeDefine charge quantization and conservation while distinguishing conductors from insulators.Charge exists in discrete multiples of the elementary charge and is strictly conserved in all interactions. Conductors allow free movement of charge carriers while insulators restrict it. These properties set the foundation for all subsequent electromagnetic behavior.
2. Coulomb's Law and ForceApply Coulomb's law to calculate forces between multiple charges in one and two dimensions.The electrostatic force between point charges follows an inverse-square law scaled by the Coulomb constant. Vector superposition yields the net force on any charge in an assembly. Worked examples demonstrate equilibrium configurations and force cancellation.
3. Electric Field ConceptCalculate electric field vectors from point charges and continuous charge distributions.Electric field is defined as force per unit charge and points away from positive charge. Integration over line, surface, and volume distributions produces field maps. Field lines provide a visual representation of direction and relative strength.
4. Gauss's Law for Electric FieldsUse Gauss's law to find electric fields for symmetric charge distributions.Gauss's law relates flux through a closed surface to enclosed charge. High-symmetry cases such as spheres, cylinders, and planes allow analytic field solutions. The law also reveals that field inside a hollow conductor is zero in electrostatic equilibrium.
5. Electric Potential and Potential EnergyCompute electric potential and relate it to potential energy and work.Potential is a scalar quantity whose negative gradient yields the electric field. Equipotential surfaces are perpendicular to field lines. Conservative nature of the electrostatic force guarantees path-independent work calculations.
6. Capacitance and Stored EnergyDerive capacitance for parallel-plate and spherical geometries and calculate stored energy.Capacitance equals charge stored per unit potential difference. Dielectrics increase capacitance by the factor kappa while reducing the net field. Energy density in the electric field is one-half epsilon zero E squared.
7. Electric Current and Ohm's LawRelate current density to drift velocity and apply Ohm's law to resistive circuits.Current is the rate of charge flow and equals the product of charge density, drift speed, and area. Resistivity arises from scattering of charge carriers. Power dissipated equals I squared R, linking electrical work to thermal energy.
8. Magnetic Field from Moving ChargeCalculate the magnetic field generated by a single moving charge or steady current.The Biot-Savart law gives the magnetic field from velocity or current elements. Direction follows the right-hand rule. The field circles the line of motion and falls as one over r squared.
9. Ampere's Law and Ampere-Maxwell CorrectionApply Ampere's law to find magnetic fields inside wires and solenoids.Ampere's law relates circulation of B to enclosed current. Symmetry permits solutions for infinite straight wires and solenoids. Maxwell's addition of displacement current ensures consistency with charge conservation and enables electromagnetic waves.
10. Faraday's Law of InductionCalculate induced emf from changing magnetic flux and apply Lenz's law.Induced emf equals the negative rate of change of magnetic flux. Lenz's law dictates that induced currents oppose the change producing them. Motional emf arises when conductors move through static fields.
11. Maxwell's Equations in Integral FormState and interpret all four Maxwell equations and their implications for fields.Gauss's laws for E and B, Faraday's law, and the Ampere-Maxwell law form a complete set. They imply that changing electric fields produce magnetic fields and vice versa. The equations unify electricity, magnetism, and optics.
12. Charge in Electromagnetic Waves and ApplicationsConnect oscillating charges to wave generation and identify practical technologies.Accelerating charges radiate electromagnetic waves whose frequency matches the oscillation rate. Antenna design, microwave cavities, and optical sources all rely on controlled charge acceleration. Energy transport occurs via the Poynting vector of the resulting fields.

Questions this course answers

Grounded in trusted sources

• National Institute of Standards and Technology
• Massachusetts Institute of Technology
• U.S. Department of Energy
• David J. Griffiths, Introduction to Electrodynamics — fields, potentials, Maxwell
• Hugh D. Young and Roger A. Freedman, University Physics — E&M chapters
• Edward M. Purcell and David J. Morin, Electricity and Magnetism — field-first approach
• MIT OCW, Electricity and Magnetism (8.02) — circuits and fields, https://ocw.mit.edu/
• OpenStax University Physics Volume 2 — E&M, https://openstax.org/details/books/university-physics-volume-2

Every Wunder lesson is built from real, reputable sources — never invented.

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