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A parallel-plate capacitor with plate separation $d$ has the space between the plates filled with two slabs of dielectric, one with constant $K_{1}$ and the other with constant $K_{2, \text { and each }}$ having thickness $d / 2$ . (a) Show that the capacitance is given by $C=\frac{2 \epsilon_{o} A}{d}\left(\frac{K_{1} K_{2}}{K_{1}+K_{2}}\right) \cdot($Hint: Can you think of this combination as two capacitors in series? (b) To see if your answer is reasonable, check it in the following cases: (i) There is only one dielectric, with constant $K,$ and it completely fills the space between the plates. (ii) The plates have nothing but air, which we can treat as vacuum, between them.

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Physics 101 Mechanics

Physics 102 Electricity and Magnetism

Chapter 18

Electric Potential and Capacitanc

Kinetic Energy

Potential Energy

Energy Conservation

Electric Charge and Electric Field

Gauss's Law

Electric Potential

Capacitance and Dielectrics

University of Washington

Hope College

University of Winnipeg

Lectures

13:02

In physics, potential energy is the energy possessed by a body or a system due to its position relative to others, stresses within itself, electric charge, and other factors. The unit for energy in the International System of Units (SI) is the joule (J). One joule is the energy expended (or work done) in applying a force of one newton through a distance of one metre (1 newton metre). The term potential energy was introduced by the 19th century Scottish engineer and physicist William Rankine, although it has links to Greek philosopher Aristotle's concepts of potentiality. Potential energy is associated with forces that act on a body in a way that the work done by these forces on the body depends only on the initial and final positions of the body, and not on the specific path between them. These forces, that are called potential forces, can be represented at every point in space by vectors expressed as gradients of a scalar function called potential. Potential energy is the energy of an object. It is the energy by virtue of a position relative to other objects. Potential energy is associated with restoring forces such as a spring or the force of gravity. The action of stretching the spring or lifting the mass is performed by a force that works against the force field of the potential. This work is stored in the field, which is said to be stored as potential energy.

18:38

In physics, electric flux is a measure of the quantity of electric charge passing through a surface. It is used in the study of electromagnetic radiation. The SI unit of electric flux is the weber (symbol: Wb). The electric flux through a surface is calculated by dividing the electric charge passing through the surface by the area of the surface, and multiplying by the permittivity of free space (the permittivity of vacuum is used in the case of a vacuum). The electric flux through a closed surface is zero, by Gauss's law.

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Um, Okay, So for this problem, we want to derive an expression for the capacitance of, um, a capacitor with to die Electric Senate. And so the trick to this problem is by considering the to die electrics to be in serious and so to model, this is a two capacitors with these two different dialect tricks in Siri's. So you're gonna model it as if you had, um, these two like this, And so k one que tu. And so, to find the equivalent capacitance of this, what you want to do is, um you just want to add in peril. Oh, so if there in Siri's, you can add them inversely so you can say one over a sea equivalent is one over, See one which is equal to Absalon. Not a times kapo one over D over, too. And then that's the same thing for the 2nd 1 But with Absalon not a capital to. And then if you solve this algebraic lee, I'm debating if I should do it, let's see. So I mean these common denominator be Capital one Kappa too. So then this would have to get multiply, and then we could put the two down here. So that's gonna be de Kappa one plus capital to just kind of getting the numerator Sze Multiplying by the numerator is by the appropriate factor to make the denominators the same. And then that's one oversee. So then you want to flip it and you got see equivalent is just what, um is given in the book to Absolute night a Kappa one cap itu all divided by de times the sum of the capas. And so you contract that if the Kappas are the same, then this nuke denominators simplifies to two, and that cancels that too. And then this just becomes, um it becomes two times at Kappa and then that cancels out a cap it here. So it's sort of passes that check. Was there anything else in the problem that they wanted to be done? Um And then if If

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