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Sketch the indicated curves and surfaces.An electric charge is so distributed that the electric potential at all points on an imaginary surface is the same. Such a surface is called an equipotential surface. Sketch the graph of the equipotential surface whose equation is $2 x^{2}+2 y^{2}+3 z^{2}=6$

Calculus 3

Chapter 29

Partial Derivatives and Double Integrals

Section 2

Curves and Surfaces in Three Dimensions

Partial Derivatives

Missouri State University

Harvey Mudd College

University of Michigan - Ann Arbor

University of Nottingham

Lectures

02:56

In mathematics, a vector (…

06:36

02:58

Charge of uniform surface …

21:10

The electric potential in …

06:49

If $V(x, y)$ is the electr…

10:23

Consider the following pot…

00:40

Two point charges are on t…

03:04

If $ V(x, y) $ is the elec…

03:42

(a) Sketch a $V$ -versus-p…

04:21

06:30

09:48

The electric field in the …

23 points on the X Y plane or the Z equals zero plane. We have a charge density, uh, eight. Nana Coombs Commuter spared. Let's call this plane A and the plane Z equals two meters called Plan B. We have three nano columns per meter squared, and we want to find what the field is at any point in the plane defined by his equals one meter and C equals three. So we have our two planes that parallel and field from a plane of charges directed away from the plane. So we just need to keep this in mind to get our science correct and that the field is all in the all of the field is Z interaction. So the magnitude of our field here is just the difference between the two fields because here at one meter, it's in between. So field from B is negative, and we've seen before how we get this expression for the field from a plane of charge using gases law and is putting the numbers in. We find that it's 2.8 two I'm 10 Squared Newtons per Coolum. The the only thing that really matters about a one meter. Here is the fact that it puts us, uh, in between them and similarly, the, uh, three meters here puts us above both. And so now they add together. So this is said a over to absolutely not plus signal be over to Absalon. So now this has a value of six point 21 times 10 squared Newtons for cooler.

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