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(1) A uniform electric field of magnitude $5.8 \times 10^{2} \mathrm{N} / \mathrm{Cpasses}$ through a circle of radius 13 $\mathrm{cm} .$ What is the electric flux through the circle when its face is $(a)$ perpendicular to the field lines, $(b)$ at $45^{\circ}$ to the field lines, and (c) parallel to the field lines?

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a) 31$N . m^{2} / C$b) 22$N . m^{2} / C$c) 0

Physics 102 Electricity and Magnetism

Chapter 22

Gauss's Law

Electric Charge and Electric Field

Electric Potential

Cornell University

Hope College

University of Sheffield

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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(1) A uniform electric fie…

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(II) A flat circle of radi…

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A flat surface with area $…

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A square surface of area $…

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01:03

In Fig. $23-37$, a butter…

01:58

A circular surface with a …

00:37

Butterfly Net In Fig. 24-2…

04:40

04:46

The electric field on the …

03:58

01:07

Uniform electric flux. Fi…

03:26

Uniform electric field. In…

Uniform electric field. I…

02:40

What's the electric f…

02:27

A 40.0 -cm-diameter circul…

Okay, so we're doing Chapter 22 problems. One here. So this problem says a uniform electric field of magnitude 5.8 tons. 10 to 2 Newtons per Coolum passes through a circle of radius, 13 centimeters. Um, so part ay. Says what is the electric flux through the circle when its face is perpendicular to the field lines? Okay, so we know that the electric flux is given by the electric field vector dotted into the normal area vector. And this thing could be written as the magnitude of these vectors times CO sign of the angle between them. So in this first case, it says, we want to calculate it when the face is perpendicular to the fuel lines. So that's corresponding to a fatal equal in zero degrees. So now we can just calculate this easily as 5.8 times tea to cool times the area, which is pi times the radius just 0.1 and three meters squared times co sign of zero, which is just one cool. So then we must plug this in our calculator here when we get an answer of 31 meter squared her cool. Awesome. So their answer for part a moving on the part beat, it says Now we want to do it when the electric flux through the circle, when it's faces 45 degrees to the field lines. So this just means our faith and our equation there becomes 45 degrees. So let's then calculate the electric flux here, and this is just five point. Think times tended to Newton's for Coolum Gardens pie 0.13 meters squared times Co. Sign of 45 degrees. Awesome. So now we can just plug this in our calculator and see for part B. R. Electric field comes out being 20 to Newton Meters Squared curriculum. Awesome. And lastly, Percy. It now says our electric flux when this face is parallel to the fuel lines. So if it's picked faces parallel to the fuel lines, that means the angle the normal angle off of the face is going to be at 90 degrees from the electric field lens. So if our coastline is 90 degrees, are angled Data's 90 degrees coastline of data, then becomes zero. And since our equation is just the magnitudes times co sign of data, we know that in this case it is zero. They had an ad on the same units. Newton meters squared for cool. Awesome. That's it

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