🧠Fields as Functions Mapping Space to Physical Quantities

A field in physics is a quantity that's defined at every single point throughout a given space, allowing these quantities to vary from one point to another. This fundamental concept is crucial across various physics branches, from electromagnetism and gravity to fluid dynamics. Whether it's a scalar field assigning a single numerical value (like temperature) or a vector field assigning both a magnitude and direction (like wind velocity) to each point, fields are essentially a map from a "base space" to a space of values. They are vital for describing physical phenomena locally, meaning the value of a field at one point doesn't directly depend on values at other points—a property known as locality, which is a cornerstone of many physical theories. While the mathematics can seem complex, you encounter fields daily, like temperature maps or weather forecasts illustrating wind patterns.

Cloud computing facilitates diverse field visualizations and analyses, offering animated results for concepts like affine spaces and charge-generated electric fields, interactive web tools for understanding volume elements and 3D scalar/vector fields, and plotting capabilities for showcasing density gradients, surface normals, and various vector field properties.

🎬Animated result and interactive web

Affine space and Coordinate System

2D-the mass of a sphere with a position-dependant density

a gravitational acceleration vector at each point in space

the mass of a sphere with a given density field

integral force density over a volume

the electric field vectors around a point charge using Gauss’s law