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Currently Playing: This physics problem is 200 years old. There's a simpler solution

Discover the physics of electric fields and conductors! 📝 Get the notes for free here: https://courses.physicswithelliot.com/notes-sign-up 📺 Learn the basics about electric fields and Gauss's law: https://youtu.be/j_tsa-uawJ0 📺 A short video about the method of images: https://youtube.com/shorts/5FTh_oDG-i0 ✉️ Sign up for my newsletter for additional physics lessons: https://courses.physicswithelliot.com/sign-up 🅿 Become a patron to help make videos like these possible: https://www.Patreon.com/PhysicsWithElliot 👨‍🏫 My full online courses: https://www.physicswithelliot.com/courses 🙋‍♀️ "What software did you use to make this video?" and other FAQs: https://www.physicswithelliot.com/faq 📖 Video summary: It's a classic problem that you'll find near the beginning of just about any college textbook on electromagnetism: a positive charge is placed above a large, conducting sheet of metal, and the question is to determine the resulting electric field. It's a hard problem, in principle: the positive charge is going to attract a whole bunch of negative charges to accumulate beneath it on the surface of the sheet, and those induced charges create their own contribution to the field. The catch is that we don't know in advance how those charges are going to distribute themselves! So how can we possibly compute the electric field if we don't even know where all the charges are? The original solution to the puzzle dates back to William Thomson—aka Lord Kelvin—in the mid-1800s, using a trick he invented called the method of images. And that trick is still how you'll typically find this problem solved in textbooks to this day. Proving why it actually works, though, requires quite a bit of fairly advanced math about boundary value problems and uniqueness theorems. But there's a simpler approach—one based on symmetry—that requires essentially nothing more than a high-school-level understanding of Coulomb's law. And that's what I'll explain in this video. Along the way, we'll learn about some of the fundamental properties of conductors, and we'll get a peek at where Kelvin's method of images comes from in the first place. 🏷️ Chapters: 0:00 Introduction 1:46 The problem 3:52 Conductors 7:43 The solution 11:43 The surface charge 14:07 A peek at the method of images 15:53 5 years If you find the content I’m creating valuable and would like to help make it possible for me to continue sharing more, please consider supporting me! You can make a recurring contribution at https://www.Patreon.com/PhysicsWithElliot, or make a one time contribution at https://www.physicswithelliot.com/support-me. Thank you so much! About me: I’m Dr. Elliot Schneider. I love physics, and I want to help others learn (and learn to love) physics, too. Whether you’re a beginner just starting out with your physics studies, a more advanced student, or a lifelong learner, I hope you’ll find resources here that enable you to deepen your understanding of the laws of nature. For more cool physics stuff, visit me at https://www.physicswithelliot.com.