Deriving Gauss's Law for Electric Flux via the Divergence Theorem from Vector Calculus скачать в хорошем качестве

Deriving Gauss's Law for Electric Flux via the Divergence Theorem from Vector Calculus

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)    • Calculus IV: Vector Calculus (Line Integra...   OTHER COURSE PLAYLISTS: ►DISCRETE MATH:    • Discrete Math (Full Course: Sets, Logic, P...   ►LINEAR ALGEBRA:    • Linear Algebra (Full Course)   ►CALCULUS I:    • Calculus I (Limits, Derivative, Integrals)...   ► CALCULUS II:    • Calculus II (Integration Methods, Series, ...   ►MULTIVARIABLE CALCULUS (Calc III):    • Calculus III: Multivariable Calculus (Vect...   ►DIFFERENTIAL EQUATIONS:    • How to solve ODEs with infinite series | I...   OTHER PLAYLISTS: ► Learning Math Series    • 5 Tips To Make Math Practice Problems Actu...   ►Cool Math Series:    • Cool Math Series   BECOME A MEMBER: ►Join:    / @drtrefor   MATH BOOKS & MERCH I LOVE: ► My Amazon Affiliate Shop: https://www.amazon.com/shop/treforbazett SOCIALS: ►Twitter (math based):   / treforbazett   ►Instagram (photography based):   / treforphotography