Flux - general not hard question

In summary, the conversation discusses the calculation of the total electric flux through the four slanted surfaces of a pyramid with a horizontal square base and a height of 4.00m. The electric field is 52.0 N/C and the angle between the normal and the vertical electric field is needed to calculate the flux. The formula \int\vec E\cdot d\vec A=EA\cos(\theta) can be used to find the flux.
  • #1
benndamann33
22
0
Question: A pyramid with horizontal square base, 6.00m on each side and a height of 4.00m is placed in a vertical electic field of 52.0 N/C. Calculate the total electric fluc through the pyramids four slanted surfaces.

I know you can figure out the flux through the base = 36 m * 52.0 N/C because it's a unform electric field so flux in base = flux out pyramid sides, but if you were to do it without using that fact, actually using the geometry of the sides and such, what angle should you be using and cosine or sine? I can't seem to work it out. Thanks
Ben
 
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  • #2
The electric field and the angle it makes with the normal to the surface is still constant over the entire pyramid side, so the flux is [itex]\int\vec E\cdot d\vec A=EA\cos(\theta)[/itex]. Where theta is the angle between the normal and the vertical electric field.
 
  • #3
jamin,

Thank you for your question. In order to calculate the total electric flux through the four slanted surfaces of the pyramid, we can use the formula for electric flux, which is given by Φ = E * A * cosθ, where E is the electric field strength, A is the area of the surface, and θ is the angle between the electric field and the surface.

In this case, the electric field is given as 52.0 N/C and the area of each slanted surface can be calculated using the Pythagorean theorem as A = 6.00m * √(6.00m)^2 + (4.00m)^2 = 6.00m * 7.21m = 43.26m^2.

Now, in order to find the angle θ, we can use trigonometric ratios. Since the pyramid has a horizontal square base, we can consider one of the slanted surfaces as a right triangle with the base as the adjacent side and the height as the opposite side. Therefore, the angle θ can be found as tanθ = 4.00m/6.00m, which gives θ = tan^-1(4.00m/6.00m) = 33.69°.

Substituting these values in the electric flux formula, we get Φ = 52.0 N/C * 43.26m^2 * cos33.69° = 1938.50 Nm^2/C. Therefore, the total electric flux through the four slanted surfaces of the pyramid is 1938.50 Nm^2/C.

I hope this helps to answer your question. Please let me know if you need any further clarification. Thank you.
 

1. What is flux?

Flux is a general physics concept that refers to the rate at which a physical quantity, such as energy or mass, flows through a given area or volume. It is represented by the symbol Φ and is measured in units of energy or mass over time.

2. How is flux calculated?

Flux is calculated by taking the product of the magnitude of the quantity being measured (such as the strength of an electric field) and the cross-sectional area through which it is flowing. The result is then multiplied by the cosine of the angle between the direction of the quantity and the normal vector to the area.

3. What is the difference between magnetic flux and electric flux?

Magnetic flux refers to the flow of magnetic field lines through a given area, while electric flux refers to the flow of electric field lines through a given area. While both are measured in units of energy or mass over time, they have different physical properties and behaviors.

4. What are some real-world applications of flux?

Flux has many applications in various fields, including physics, engineering, and biology. For example, it is used to calculate the rate of heat transfer in thermodynamics, the strength of electric and magnetic fields in electrical engineering, and the flow of particles in fluid dynamics.

5. How does flux relate to the laws of conservation of energy and mass?

Flux is closely related to the laws of conservation of energy and mass, which state that these quantities cannot be created or destroyed, only transformed. Flux is a measure of the flow of these quantities, and therefore must be conserved in any physical system according to these laws.

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