In mathematics and physics, an equipotential or isopotential refers to a region in space where every point is at the same potential. This usually refers to a scalar potential (in that case it is a level set of the potential), although it can also be applied to vector potentials. An equipotential of a scalar potential function in n-dimensional space is typically an (n − 1)-dimensional space. The del operator illustrates the relationship between a vector field and its associated scalar potential field. An equipotential region might be referred as being 'of equipotential' or simply be called 'an equipotential'. An equipotential region of a scalar potential in three-dimensional space is often an equipotential surface (or potential isosurface), but it can also be a three-dimensional mathematical solid in space. The gradient of the scalar potential (and hence also its opposite, as in the case of a vector field with an associated potential field) is everywhere perpendicular to the equipotential surface, and zero inside a three-dimensional equipotential region. Electrical conductors offer an intuitive example. If a and b are any two points within or at the surface of a given conductor, and given there is no flow of charge being exchanged between the two points, then the potential difference is zero between the two points. Thus, an equipotential would contain both points a and b as they have the same potential. Extending this definition, an isopotential is the locus of all points that are of the same potential. Gravity is perpendicular to the equipotential surfaces of the gravity potential, and in electrostatics and steady electric currents, the electric field (and hence the current, if any) is perpendicular to the equipotential surfaces of the electric potential (voltage). In gravity, a hollow sphere has a three-dimensional equipotential region inside, with no gravity from the sphere (see shell theorem). In electrostatics, a conductor is a three-dimensional equipotential region. In the case of a hollow conductor (Faraday cage), the equipotential region includes the space inside. A ball will not be accelerated left or right by the force of gravity if it is resting on a flat, horizontal surface, because it is an equipotential surface.For the gravity of Earth, the corresponding geopotential isosurface that best fits mean sea level is called the geoid. (Wikipedia).
The method of determining eigenvalues as part of calculating the sets of solutions to a linear system of ordinary first-order differential equations.
From playlist A Second Course in Differential Equations
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Visit http://ilectureonline.com for more math and science lectures! In this video I will explain and show (in general) what is and how to find an eigenvector. Next video in this series can be seen at: https://youtu.be/SGJHiuRb4_s
From playlist LINEAR ALGEBRA 3: EIGENVALUES AND EIGENVECTORS
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10A An Introduction to Eigenvalues and Eigenvectors
A short description of eigenvalues and eigenvectors.
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A11 Eigenvalues with complex numbers
Eigenvalues which contain complex numbers.
From playlist A Second Course in Differential Equations
A08 Example problem of repeated real eigenvalues
Here is an example problem with repeated eigenvalues.
From playlist A Second Course in Differential Equations
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In this lecture, we define eigenvectors and eigenvalues of a square matrix. We also prove a couple of useful theorems related to these concepts.
From playlist Linear Algebra Lectures
With the eigenvalues for the system known, we move on the the eigenvectors that form part of the set of solutions.
From playlist A Second Course in Differential Equations
Generalized eigenvectors. Generalized eigenspaces. Generalized eigenvectors corresponding to distinct eigenvalues are linearly independent.
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The electric potential difference in a uniform electric field is derived and used to show lines of equal electric potential or equipotential lines. Equipotential lines and surfaces of point charges and dipoles are shown. The equation for the electric potential of a point charge is discusse
From playlist All of AP Physics C: Electricity & Magnetism!
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This video covers Section 19.4 of Cutnell & Johnson Physics 10e, by David Young and Shane Stadler, published by John Wiley and Sons. The lecture is part of the course General Physics - Life Sciences I and II, taught by Dr. Boyd F. Edwards at Utah State University. This video was produced
From playlist Lecture 19B. Electric Potential Energy and the Electric Potential
036 - Equipotential Lines In this video Paul Andersen explains how equipotential lines show equal electric potential in an electric field. Equipotential lines can be created from scalar values or by observing the electric field lines. An charged object can move along a equipotential lin
From playlist AP Physics 2 Videos
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AP Physics C: Electricity and Magnetism review of Electric Potential including: derivation of electric potential energy, derivation of electric potential and electric potential difference, a discussion of the electronvolt, electric potential difference in a constant electric field, equipot
From playlist AP Physics C: Electricity & Magnetism Review
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This physics video tutorial provides a basic introduction into equipotential lines and equipotential surfaces. It discusses the relationship between equipotential lines and electric field. It discusses how to calculate the work done by a charge as it moves across an equipotential surface
From playlist New Physics Video Playlist
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Demonstrating the equipotential lines of an electric dipole. https://www.flippingphysics.com/ap-physics-c.html #physics #dipole #equipotential
From playlist Vertical Videos
PHYS 102 | Potential and Field 1 - Equipotential Surface
You integrate the field to get the potential. This leads to a useful mathematical tool - the equipotential surface. It is more useful than the name implies, as you will see here. -----Electric Potential Playlist - https://www.youtube.com/playlist?list=PL9_sR6QqqcymuuH4gQhg5kSmyePmGcX3h -
From playlist PHYS 102 | Electric Potential
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Visit http://ilectureonline.com for more math and science lectures! In this video I will explain equipotential surfaces and the change in potential and work in between the surfaces.
From playlist PHYSICS 38 ELECTRICAL POTENTIAL
MIT RES.TLL-004 STEM Concept Videos View the complete course: http://ocw.mit.edu/RES-TLL-004F13 Instructor: John McGreevy This video begins with a review of electric field and electric potential, focusing on their similarities and differences and the way they are most commonly represented
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Physics - E&M: Ch 38.1 Voltage Potential Understood (16 of 24) What is an Equipotential Line?
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain what is an equipotential line where potentials=voltage and equi=equal or unchanging. In other words, a line alone which the voltage doesn't change. In this example there is a 2-dimensional pla
From playlist PHYSICS 38.1 VOLTAGE UNDERSTOOD
A09 Example problem of multiplicity two
Example problem solving a set of differential ordinary differential equations with two identical eigenvalues.
From playlist A Second Course in Differential Equations