Tag «integral»

Matter & Interactions II, Week 5

This week was all about calculating electric fields for continuous charge distributions. This is usually students’ first exposure to what they think of as “calculus-based” physics because they are explicitly setting up and doing integrals. There’s lots going on behind the scenes though. In calculus class, students are used to manipulating functions by taking their …

Conceptual Understanding in Introductory Physics XXI: Deriving Expressions for Kinetic Energy

Okay this may not be the most interesting thing to think about, but it’s a question I’ve been asked on several occasions. For that reason alone, I started thinking about it. I also think it’s another situation where coordinate-free vector manipulation can simplify otherwise messy questions and problems. So, here’s the question. Give three different …

Conceptual Understanding in Introductory Physics XVIII: The Maxwell Equations

The Maxwell equations contain everything mentioned in an introductory calculus-based electromagnetic theory course, and then some. They contain detailed mathematical structure and deep insight into electromagnetic fields. They are a magnificent playground for learning the various theorems of vector calculus, and applying these theorems to the fields of particles naturally leads to things like divergence, …

Mastodon