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A capacitor consists of two parallel plates, each with an area of 16.0 $\mathrm{cm}^{2}$ , separated by a distance of 0.200 $\mathrm{cm} .$ The material that fills the volume between the plates has a dielectric constant of $5.00 .$ The plates of the capacitor are connected to a $300-\mathrm{V}$ battery. (a) What is the capacitance of the capacitor? (b) What is the charge on either plate? (c) How much energy is stored in the charged capacitor?

a) $3.54 \times 10^{-11} \mathrm{F}$b) $1.0625 \times 10^{-8} \mathrm{C}$c) $1.593 \times 10^{-6} \mathrm{J}$

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

Rutgers, The State University of New Jersey

Simon Fraser University

Hope College

McMaster University

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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04:03

Okay, so this question is a pretty classic one. Um, so we have the area of the plates, so that's 16 centimeters squared some to go ahead and convert that two meters squared by multiplying by 10 to the minus. For, um, I'm not gonna go over how to do that. I would just google it. Um, this problem's already kind of long separated by a distance of point thio centimeters so point two times 10 to the minus two meters in the dye. Electric constant is five and the plates are connected. Thio a 300 volt battery. And we want to get the capacitance. So a C is just equal to Absalon, not a divided by d. So, um, I can remember these numbers. Absolutely not. Time. 16 time scent of the minus for divided by point 02 7.8 times 10 to the minus 12 Sherrod. And for part B, we are look oh, they see double truck My enter actually for part one. So 16 miles for me. So not a over d Oh, I forgot my to include cafa. So I need to multiply by five. Well, we will keep this time some of the minus 12. Maybe so. 35.4 times 10 to the minus 12. And for B, we want the charge. So see, is cured me. So, um, cure is equal to C. B. So we just need to take this capacitance and multiply it by 300 to get the charge. When I did that, I got one point. 06 times kind of the minus eight Crooms and report See how much energy is stored. So just use 1/2 Q We so 300 times the charge divided by two. Oh, I got 1.59 times 10 to the minus six. Jules.

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