Calculus IV: Vector Calculus (Line Integrals, Surface Integrals, Vector Fields, Greens' Thm, Divergence Thm, Stokes Thm, etc) **Full Course** Deriving Gauss's Law for Electric Flux via the Divergence Theorem from Vector Calculus
Deriving Gauss's Law for Electric Flux via the Divergence Theorem from Vector Calculus Transcript and Lesson Notes
I love this application of vector calculus. We are going to derive one of the foundational laws in electricity and magnitism called Gauss' Law, which is one of Maxwell's four equations that govern E&M. This is a property
Quick Summary
I love this application of vector calculus. We are going to derive one of the foundational laws in electricity and magnitism called Gauss' Law, which is one of Maxwell's four equations that govern E&M. This is a property
Key Takeaways
- Review the core idea: I love this application of vector calculus. We are going to derive one of the foundational laws in electricity and magnitism called Gauss' Law, which is one of Maxwell's four equations that govern E&M. This is a property
- Understand how Gauss' Law fits into Deriving Gauss's Law for Electric Flux via the Divergence Theorem from Vector Calculus.
- Understand how Divergence Theorem fits into Deriving Gauss's Law for Electric Flux via the Divergence Theorem from Vector Calculus.
- Understand how vector calculus fits into Deriving Gauss's Law for Electric Flux via the Divergence Theorem from Vector Calculus.
- Understand how electric field fits into Deriving Gauss's Law for Electric Flux via the Divergence Theorem from Vector Calculus.
Key Concepts
Full Transcript
I love this application of vector calculus. We are going to derive one of the foundational laws in electricity and magnitism called Gauss' Law, which is one of Maxwell's four equations that govern E&M. This is a property of the divergence theorem, which we studied in the previous video in the special case when the divergence is zero. This let's the outward flux of an electric field across any surface containing a charged particle be equated to the outward flux of the electric field across the sphere of radius a, and we are able to compute that pretty easily in this video giving us Gauss' Law. If you are watching my playlist primarily from he perspective of vector calculus then this video can be skipped, but if you have any interest in physics or engineering where you might see E&M, then it really is one of the coolest application. MY VECTOR CALCULUS PLAYLIST: ►VECTOR CALCULUS (Calc IV) https://www.youtube.com/playlist?list=PLHXZ9OQGMqxfW0GMqeUE1bLKaYor6kbHa OTHER COURSE PLAYLISTS: ►DISCRETE MATH: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS ►LINEAR ALGEBRA: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxfUl0tcqPNTJsb7R6BqSLo6 ►CALCULUS I: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxfT9RMcReZ4WcoVILP4k6-m ► CALCULUS II: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxc4ySKTIW19TLrT91Ik9M4n ►MULTIVARIABLE CALCULUS (Calc III): https://www.youtube.com/playlist?list=PLHXZ9OQGMqxc_CvEy7xBKRQr6I214QJcd ►DIFFERENTIAL EQUATIONS: https://www.youtube.com/watch?v=xeeM3TT4Zgg&list=PLHXZ9OQGMqxcJXnLr08cyNaup4RDsbAl1 OTHER PLAYLISTS: ► Learning Math Series https://www.youtube.com/watch?v=LPH2lqis3D0&list=PLHXZ9OQGMqxfSkRtlL5KPq6JqMNTh_MBw ►Cool Math Series: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxelE_9RzwJ-cqfUtaFBpiho BECOME A MEMBER: ►Join: https://www.youtube.com/channel/UC9rTsvTxJnx1DNrDA3Rqa6A/join MATH BOOKS & MERCH I LOVE: ► My Amazon Affiliate Shop: https://www.amazon.com/shop/treforbazett SOCIALS: ►Twitter (math based): http://twitter.com/treforbazett ►Instagram (photography based): http://instagram.com/treforphotography
Lesson FAQs
What is Deriving Gauss's Law for Electric Flux via the Divergence Theorem from Vector Calculus about?
I love this application of vector calculus. We are going to derive one of the foundational laws in electricity and magnitism called Gauss' Law, which is one of Maxwell's four equations that govern E&M. This is a property
What key concepts are covered in this lesson?
The lesson covers Gauss' Law, Divergence Theorem, vector calculus, electric field, electric flux.
What should I learn before Deriving Gauss's Law for Electric Flux via the Divergence Theorem from Vector Calculus?
Review the previous lessons in Calculus IV: Vector Calculus (Line Integrals, Surface Integrals, Vector Fields, Greens' Thm, Divergence Thm, Stokes Thm, etc) **Full Course**, then use the transcript and key concepts on this page to fill any gaps.
How can I practice after this lesson?
Practice by applying the main concepts: Gauss' Law, Divergence Theorem, vector calculus, electric field.
Does this lesson include a transcript?
Yes. The full transcript is visible on this page in indexable HTML sections.
Is this lesson free?
Yes. CourseHive lessons and courses are available to learn online for free.
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