Gauss Law and Flux: Calculate Charge Inside Box

In summary, the closed box shown in the figure has a horizontal and rightward electric field everywhere, with values of E1=90 V/m on the left side, E2=400 V/m on the right slanting side, E3=120 V/m on the top, E4=175 V/m on the front and back, and E5=245 V/m on the bottom. The accurate value of ε0=8.85e-12 C2/N·m2 is used to determine the charge inside the box, which can be found by using the geometry of a right triangle to calculate the cosine of the angle and multiplying it by the area of the slant rectangle. The net flux through the closed surface is
  • #1
Kreamer
22
0

Homework Statement


The electric field has been measured to be horizontal and to the right everywhere on the closed box shown in the figure. All over the left side of the box E1 = 90 V/m, and all over the right, slanting, side of the box E2 = 400 V/m. On the top the average field is E3 = 120 V/m, on the front and back the average field is E4 = 175 V/m, and on the bottom the average field is E5 = 245 V/m.

22-104-HW_prism_sym.jpg


How much charge is inside the box? Use the accurate value ε0 = 8.85e-12 C2/N·m2.


The Attempt at a Solution


I have been working these homework problems no problem when it is just rectangles and cylinders and other shapes where Nhat and E both point in the same direction, however I thought that when it was not the same you had to use cosin of the angle made between Nhat and E. However it does not give me an angle. Am I going about this the wrong way?
 
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  • #2
It doesn't give you the angle, but it gives enough information for you to find the cosine of the angle from the geometry of a right triangle.
 
  • #3
I asked a friend after posting this. They said you use the area of the left side and multiply it by the electric field coming out of the slope as if it was just a rectangle and there was no slope at all. No need for any cosin or angles at all. I tried this and it gave me the right answer but I am still confused as to how it works?
 
  • #4
The cosine of the angle is 4/12, multiply (4/12) times the area of the slant rectangle, 12×5, gives the area of the vertical rectangle.
 
  • #5
ahh clever
 
  • #6
I don't understand, isn't it just 0? The net flux through a closed surface is not 0 here?
 
  • #7
flyingpig said:
I don't understand, isn't it just 0? The net flux through a closed surface is not 0 here?
It doesn't say anything about charge inside. Only gives E field at the various surfaces.
 
  • #8
The next flux would be zero if the E field had the same value at E1 and E2 ,
but since they have different E field values at those points it is not zero.
 

What is Gauss Law and Flux?

Gauss Law is a fundamental law in electrostatics that describes the relationship between electric charge and the electric field. Flux is a measure of the amount of electric field passing through a given surface.

How do you calculate Gauss Law?

Gauss Law can be calculated by taking the integral of the electric field over a closed surface and equating it to the total charge enclosed by that surface.

What is the formula for calculating Flux?

The formula for calculating Flux is Φ = ∫E⋅dA, where E is the electric field and dA is an infinitesimal element of surface area.

What are some applications of Gauss Law and Flux?

Gauss Law and Flux have many applications in the field of electromagnetism, including in the design of capacitors, antennas, and electric circuits. They are also used in the study of electric fields and their effects on charged particles.

How do you calculate the charge inside a box using Gauss Law and Flux?

To calculate the charge inside a box using Gauss Law and Flux, first choose a closed surface that encloses the box. Then, calculate the flux through that surface and equate it to the total charge enclosed by the surface. This will give you the value of the charge inside the box.

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