Gauss' Law and electric flux

In summary: It gives you a relationship between the charge inside a closed surface and the flux passing through the surface. In summary, the electric flux through a rectangular box with a charge Q inside can be calculated by adding up the flux values through each of the six surfaces: Φ1=+1500, Φ2=+2200, Φ3=+4600, Φ4=-1800, Φ5=-3500, and Φ6=-5400. To find Q, the formula ΦE =Q/ε can be used, where ε is the permittivity of the medium enclosed by the surface. The total flux will be non-zero, indicating that the charge inside is also non-zero, in accordance with
  • #1
Joules23
33
0

Homework Statement


A charge Q is located inside a rectangular box. The electric flux through each of the six surfaces of the box is: Φ1=+1500 Φ2=+2200 Φ3=+4600 Φ4=-1800 Φ5=-3500 Φ6=-5400.
(unit: N x m^2/C)
What is Q?

Homework Equations



ΦE =Q/ε

The Attempt at a Solution


Add up all the Φ's to get -2400, then use ε0Φ=Q

(-2400)(8.85x10^-12) = -2.124 x 10^-8 C
 
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  • #2
What are you supposed to do? Find Q? ε is a constant usually denoted [tex] \epsilon_0[/tex].
 
  • #3
yes I am supposed to find Q

Hows this:
Add up all the Φ's to get -2400, then use ε0Φ=Q

(-2400)(8.85x10^-12) = -2.124 x 10^-8 C
 
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  • #4
Joules23 said:
yes I am supposed to find Q .. and [tex] \epsilon_0[/tex], accordning to my book is the permittivity of free space, and really doesn't say much else about it

[tex]\epsilon[/tex] is the permittivity of the medium enclosed by the surface which, in this case is the rectangular box. If the medium is air than it is equal to the permittivity of free space denoted by [tex]\epsilon_0[/tex]. For more info about permittivity see http://en.wikipedia.org/wiki/Permittivity


You should start by thiking what does Gauss' law state? What does each quantity in the formula of the law represent?

EDIT: looks like you solved it
 
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  • #5
is that right? i thought i was supposed to get zero?
 
  • #6
Joules23 said:
is that right? i thought i was supposed to get zero?
Why would you get zero?
 
  • #7
I was reading this, and it seems similar to my problem

Picture1.png
 
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  • #8
In this problem the total flux through the surface of the box is 0, so the electric charge inside it will be 0.

In your problem the total flux is non-zero so the charge inside will be non-zero.

This is exactly what Gauss' law is all about.
 

1. What is Gauss' Law and how does it relate to electric flux?

Gauss' Law is a fundamental law of electromagnetism that relates the electric flux through a closed surface to the enclosed electric charge. It states that the electric flux through a closed surface is proportional to the electric charge enclosed by that surface. This law helps us understand the behavior of electric fields and is often used to solve problems involving electric charges and fields.

2. How is Gauss' Law mathematically expressed?

Gauss' Law is expressed mathematically as:∮E⃗ ⋅ dA⃗ = Qenc/ε0where ∮E⃗ ⋅ dA⃗ represents the flux of the electric field through a closed surface, Qenc is the enclosed electric charge, and ε0 is the permittivity of free space. This equation is also known as the integral form of Gauss' Law.

3. What is electric flux and how is it calculated?

Electric flux is a measure of the electric field passing through a given area. It is calculated by taking the dot product of the electric field and the area vector. Mathematically, it can be expressed as:ΦE = E⃗ ⋅ A⃗where ΦE represents the electric flux, E⃗ is the electric field, and A⃗ is the area vector. The unit of electric flux is volt-meters (V∙m) or newton-meters squared per coulomb (N∙m²/C).

4. Can Gauss' Law be applied to any closed surface?

Yes, Gauss' Law can be applied to any closed surface, as long as it encloses the electric charge of interest. This includes any shape, such as a sphere, cube, or irregular shape. However, it is important to choose a closed surface that simplifies the calculation of the electric flux, as some surfaces may be more complex to work with than others.

5. How is Gauss' Law used in practical applications?

Gauss' Law has many practical applications, such as in the design and analysis of electrical circuits, capacitors, and electric motors. It is also used in the development of technologies such as electrostatic precipitators, which are used to remove pollutants from industrial exhaust gases. Additionally, Gauss' Law is essential in understanding the behavior of lightning and in predicting the strength of electric fields in thunderstorms.

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