Troubleshooting Nonuniform Electric Fields: Calculating Enclosed Charge

In summary: Here is a hint: think about how to solve for the flux in terms of the charge and surface area it is passing through. In summary, you need to integrate E*dA over the surface area it is going through to find the charge.
  • #1
kdp58
2
0
i am trying to calculate the enclosed charge but i am having trouble figuring out how to integrate E. E is said to be nonuniform and given by the equation E= (a + bx^2)i where a = 4 n/c and b = 2 n/c*m^2. What exactly do i integrate here? i am very confused. (ps. i have the surface area that the electric field is flowing through perpendicularly... any help would be greatly appreciated!

thanks
 
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  • #2
Your question is not clear.
Explain the symbols, at least. What is x, what is the surface, what is i.
Try to write things clearly.
Eventually, write down the exact question in full, exactlt as you have been asked it.
 
  • #3
Welcome to PF! please take a second to read the sticky (its the first thread entitled "Read this before posting")
please don't double post your problems...
 
Last edited by a moderator:
  • #4
Gauss's Law

(I merged the two threads into one.)

Here's a hint: You are looking to apply Gauss's law, which relates the electric flux through a closed surface with the charge enclosed. Look it up!

As MathStudent advises, read the sticky. Show your work and you'll get plenty of help. Give it a shot.
 
  • #5
here's the problem...

ok... the problem says that there is an enclosed surface with a=b=.436 m and c=.582 m. (forming a rectangular prism)

the electric field is passing perpendicularly through the surface a*b which is .190 m^2

it goes on to say that the electric field is non uniform and is given by the equation E=(alpha + beta*x^2)i where alpha = 4 N/C and beta =2 N/C*m^2

I am trying to calculate the enclosed charge...

I know that:
flux = sum of E * delta A
flux = charge/ epsilon0
so sum of electric field * surface area it is going through = charge/epsilon0?

charge = sum of electric field * surface area it is going through * epsilon0

and to get the sum of the electric field i feel like i need to take the integral of that equation for E above with alpha and beta... is this right? and I'm not exactly sure how to integrate this equation... help! and thank you guys so much
 
  • #6
kdp58 said:
ok... the problem says that there is an enclosed surface with a=b=.436 m and c=.582 m. (forming a rectangular prism)

the electric field is passing perpendicularly through the surface a*b which is .190 m^2
To find the flux through that surface you need to "integrate" E*dA over the surface. But where is surface a*b? It's location is important, since the field varies with x coordinate.

Hint: The only surfaces with non-zero flux are those that have some component of the field perpendicular to them. If I picture your closed surface correctly, you have two surfaces with non-zero flux, both having area a*b. But where are they?
 

1. What is an electric field?

An electric field is a force field that surrounds an electrically charged particle or object. It exerts a force on other charged particles or objects within its field.

2. How is an electric field measured?

The strength of an electric field is measured in units of volts per meter (V/m). This represents the amount of force that would be exerted on a charged particle placed in the electric field.

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

An electric field is a force field, while an electric potential is the amount of work required to move a unit of charge from one point to another in an electric field. In other words, an electric field is a measure of the force acting on a charge, while electric potential is a measure of the energy associated with that force.

4. How does distance affect an electric field?

The strength of an electric field is inversely proportional to the square of the distance from the source of the field. This means that as the distance increases, the strength of the electric field decreases.

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

Electric fields are used in a variety of everyday devices such as televisions, computers, and cell phones. They are also used in medical devices such as MRI machines and defibrillators. Additionally, electric fields are used in power generation and transmission, as well as in various types of motors and generators.

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