Electric Field; quick question

In summary, Gauss' law states that the net number of electric field lines exiting a closed, hypothetical Gaussian surface is proportional to the charge within that surface, and the constant of proportionality is 1/ε0. This can be used to find the total charge within a surface if you know the net flux and the constant of proportionality.
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popo902
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Homework Statement


A charged particle is held at the center of two concentric conducting spherical shells. Figure a shows a cross section. Figure b gives the net flux Φ through a Gaussian sphere centered on the particle, as a function of the radius r of the sphere. The scale of the vertical axis is set by Φs = 2.4 × 105 N•m2/C. What is the net charge (in Coulombs) of shell B?

heres the picture:
http://i36.photobucket.com/albums/e47/jo860/q18.jpg

Homework Equations


The Attempt at a Solution



Do i take the flux from each section and add them up?
Because in the tutor, it said that the net flux for a gaussian shell with radius r in between the radius of shell a and b was just the flux in between them and not the flux between them + the flux inside shell a
so I am a little confused...
becaus i thot net flux was ALL the flux inside that radius r summed up
 
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Perhaps I can help by just discussing Guass' law, and what it means.

Guass' law.
[tex] \oint_S \vec E \cdot d \vec A = \Phi_{electric} = \frac{Q_{enc}}{\epsilon_0} [/tex]

Let's start with just discussing what electric flux is. Electric flux is the the number of electric field lines passing through some area. Keeping general (using a surface that is not necessarily closed),

[tex] \Phi_{electric} = \int_S \vec E \cdot d \vec A [/tex]

But you need to have some sort of area to have flux. Imagine you have a small hoop that you could fit in the palm of your hand, and you bring it near an electric charge. The flux through that hoop is the total number of electric field lines passing through that hoop. If you bring the hoop closer to the charge, the flux increases. If you keep the hoop at a constant distance from the charge, and increase the hoop's radius, the flux increases. You can also change the amount of electric field lines passing through the hoop by changing the hoop's orientation. So,
...(a) If the electric field intensity increases, the flux through the hoop increases.
...(b) If the area of the hoop increases, the flux through the hoop increases.
...(c) The more parallel the hoop's normal is to the electric field lines, the greater the flux.
And keep in mind, there might be electric field lines throughout all of 3D space. But concerning the flux, the only thing that matters is the surface in question (in this case, the surface defined by the hoop). If electric field lines don't pass through the hoop, they don't matter and don't effect the flux through the hoop.

Now let's move on to a closed surface. Instead of a hoop, let's enclose the charge in a hypothetical, spherical shell (not a real shell -- just use your mind's eye to make the shell). This hypothetical shell is called a Gaussian surface. The sum of all the electric field lines exiting this surface (from the inside out), minus all the electric field lines entering this surface (from the outside in), is the total flux.

Suppose we have a charge in this Guassian surface, and vary the radius. Suppose we increase the radius of this hypothetical, spherical shell (even though the amount of charge inside remains the same). The area increases, so the flux should increase too, right? No. As the radius increases, the electric field strength decreases proportionally so that the total flux remains constant (as long as the amount of charge within the surface remains constant). Another way to look at it is if you add up all the electric field lines exiting the surface minus the lines entering the surface, the size of the surface makes no difference (one again, assuming that the total amount of charge inside the surface remains constant). This is the essence of Gauss' law.

Okay, what if there is no charge inside the Guassian surface, but there is a charge just outside of it? Well, every electric field line that enters the surface will also leave the surface at some other point. So the total lines leaving minus the total lines entering equals zero. So in conclusion:

Gauss's law states that the net number of electric field lines exiting the closed, hypothetical, Gaussian surface, is proportional to the charge within that surface (charges outside the surface don't matter). And the constant of proportionality is 1/ε0.

So use Guass' law to find the total charge within the surface. Then, if you happen to know that there are two charges within that surface, and you know the value of one of them, the other must be...?

And if you calculate the total charge within a Gaussian surface at a different radius, and you know that there are three charges within that surface, and you know the value of two of them, the third must be...?
 
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1. What is an electric field?

An electric field is a force field that is created by electrically charged particles. It is a vector quantity, meaning it has both magnitude and direction, and is measured in units of newtons per coulomb (N/C).

2. How is an electric field created?

An electric field is created when a charged particle, such as an electron or proton, interacts with another charged particle. The strength of the electric field depends on the magnitude of the charges and the distance between them.

3. What is the difference between an electric field and an electric potential?

While an electric field is a force field created by charged particles, an electric potential is the amount of work that must be done to move a charged particle from one point to another in an electric field. In other words, electric potential is a measure of the potential energy per unit charge at a given point in the electric field.

4. How is an electric field measured?

An electric field can be measured using a device called an electric field meter or voltmeter. These devices measure the strength of the electric field in a given area and provide a numerical value for the electric field strength.

5. What are some real-life applications of electric fields?

Electric fields have many practical applications, such as in electrical circuits, electric motors, and generators. They are also used in medical devices such as MRI machines, and in technologies like touchscreens and computer screens.

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