Lecture 113: Magnetic Fields from Wires and Loops—The Full Story

In this lecture, we start from the magnetic force between moving charges and work our way up to the Biot–Savart law—the foundational equation that tells us how currents generate magnetic fields. We apply this law to calculate the magnetic field around a long straight wire and along the axis of a current loop, culminating in a derivation of Ampère’s Law. Along the way, we explore the symmetry of magnetic fields, contrast them with electric fields, and connect these results to the magnetic dipole moment. Whether you're a conceptual learner or preparing for calculus-based physics, this lecture lays the groundwork for understanding how magnetic fields really emerge from electric currents.

(NEW) Study guide with screenshots for this lecture is here:
https://drive.google.com/file/d/1ivj_...

Problem set for this lecture is here:
https://drive.google.com/file/d/18oNE...

Problem set solution guide is here:
https://drive.google.com/file/d/1Krfy...

Chapters:
00:00 Introduction – Why Do Currents Create Magnetic Fields?
01:17 The Magnetic Force Between Moving Charges
02:35 Deriving the Biot–Savart Law
06:15 Applying Biot–Savart to a Long Straight Wire
13:55 Magnetic Field from a Circular Current Loop
20:45 The Dipole Field and the Magnetic Moment
24:30 Biot–Savart vs. Newton’s Third Law?
31:55 Ampère’s Law from the Straight Wire
36:50 The Big Picture – Magnetic Field Lines and Maxwell’s Equations
41:00 What’s Next – Where Magnetism in Matter Comes From