Laplace Force Course

Lesson 1 • Electric and Magnetic Field Concepts

Defines electric and magnetic fields as vector quantities. Connects field representations to the forces they exert on charged particles.

Lesson 2 • Electric Charge and Current Basics

Introduces charge quantization, current flow, and charge conservation. Establishes the physical quantities that drive all subsequent force calculations.

Lesson 3 • Vector Mathematics for Field Analysis

Reviews dot products, cross products, and coordinate systems essential for force calculations. Provides the algebraic toolkit used throughout the course.

Lesson 1 • Circular and Helical Particle Motion

Analyzes trajectories of charged particles in uniform magnetic fields. Connects centripetal acceleration to magnetic force for radius and period calculations.

Lesson 2 • Energy Considerations in Magnetic Force

Demonstrates that the magnetic force does no work on a moving charge. Clarifies the distinction between force direction and energy transfer.

Lesson 3 • Combined Electric and Magnetic Forces

Extends the force law to include simultaneous electric and magnetic fields. Students resolve total force vectors in multi-field environments.

Lesson 1 • Force on a Straight Conductor Segment

Applies the Laplace force formula to finite straight conductors in uniform fields. Students calculate magnitude, direction, and resultant force components.

Lesson 2 • Force on Curved and Irregular Conductors

Extends force calculation to non-straight conductors via line integration. Students set up and evaluate integrals for arcs and arbitrary paths.

Lesson 3 • Force on a Closed Current Loop

Proves that the net Laplace force on a closed loop in a uniform field is zero. Introduces the concept of torque as the dominant mechanical effect.

Lesson 1 • Torque on a Rectangular Current Loop

Derives torque from paired Laplace forces on opposite sides of a rectangular loop. Provides the foundational model for electric motor operation.

Lesson 2 • Force on a Dipole in Non-Uniform Fields

Shows that a magnetic dipole experiences a net translational force only in non-uniform fields. Connects gradient of field to dipole force.

Lesson 3 • Magnetic Dipole Moment

Defines the magnetic dipole moment vector for current loops of any shape. Connects dipole moment to torque and field interaction compactly.

Lesson 1 • Force Between Non-Parallel Conductors

Extends force analysis to skewed and perpendicular wire configurations. Students use vector integration to find resultant forces and torques.

Lesson 2 • Force Between Two Parallel Conductors

Applies the Laplace force law using the field of one wire acting on the other. Derives the force-per-unit-length formula and attraction/repulsion rules.

Lesson 3 • Magnetic Field of an Infinite Straight Wire

Derives the field magnitude and direction around a long straight conductor using Ampere's law. Provides the field source for inter-conductor force analysis.

Lesson 1 • Linear Actuators and Rail Guns

Models linear force production using the Laplace force on a sliding conductor in a magnetic field. Connects force, current, and field to acceleration.

Lesson 2 • Loudspeaker and Voice Coil Actuators

Analyzes the voice coil as a Laplace force transducer converting current to linear displacement. Students calculate force sensitivity and frequency response basics.

Lesson 3 • Torque Ripple and Force Uniformity

Identifies sources of torque ripple in real machines and methods to minimize them. Connects coil geometry and winding distribution to force uniformity.

Lesson 4 • Back-EMF and Power Balance

Derives back-EMF from conductor motion in a magnetic field and relates it to mechanical power. Students apply energy conservation to motor circuits.

Lesson 1 • Hall Effect Sensors

Derives the Hall voltage from Laplace force equilibrium on charge carriers in a conductor. Connects Hall voltage to magnetic field and current density.

Lesson 2 • Galvanometer and Moving-Coil Meter

Explains deflection of a current-carrying coil in a radial magnetic field as a direct Laplace force application. Derives sensitivity and full-scale deflection.

Lesson 3 • Force-Balance and Watt Balance Instruments

Examines precision instruments that null Laplace force against gravity or mechanical force. Connects force measurement to fundamental constant determination.

Lesson 1 • Finite Element Analysis for Force Prediction

Introduces numerical field simulation as a tool for accurate Laplace force prediction in complex geometries. Students interpret FEA results and validate with analytical models.

Lesson 2 • System Integration and Design Review

Synthesizes all course concepts into a structured design review process for electromagnetic force systems. Students evaluate trade-offs and document design decisions.

Lesson 3 • Thermal Limits and Current Density

Relates conductor current density to Joule heating and maximum allowable Laplace force. Students apply thermal constraints to conductor sizing.

Lesson 4 • Magnetic Circuit Analysis for Force Design

Applies magnetic circuit concepts to predict flux density in air gaps where Laplace force acts. Students size cores, gaps, and windings for target force output.