Electric Flux of equilateral triangle

In summary, the flux of a uniform electric field E=8 N/C through an equilateral triangle with side a=1m, where the normal vector makes a 60 degree angle with the direction of the electric field, can be calculated using the formula \phi=EAcosø. The angle ø in the formula is determined by the angle between the field and the normal direction, and is equal to 0 when the angle is 0 degrees and equal to 90 degrees when the angle is 90 degrees.
  • #1
msampsel
2
0

Homework Statement


What is the flux of the uniform electric field E=8 N/C through an equilateral triangle with the side a=1m, if the normal vector makes 60 degrees to the direction of the electric field.

Homework Equations


[itex]\phi[/itex]=EAcosø

The Attempt at a Solution


E=8 N/C
A= √3/4 m^2

Is the ø in this equation 60 degrees or 90-60 = 30 degrees?
 
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  • #2
Hello msampsel. Welcome to PF!

See if you can answer this question by considering a couple of special examples:

(1) What should the flux be if the angle between the normal and the field is 0? What value of ø in the formula will give this result?

(2) What should the flux be if the angle between the normal and the field is 90? What value of ø in the formula will give this result?
 
  • #3
(1) The flux would be the product of the field and the area (EA) because they are perpendicular to the plane. The value of ø would be 0 because cos(0)=1.

(2) The flux would be 0 because the field would then be parallel to the plane. The value of ø would be 90 because cos(90)=0.
 
  • #4
OK, good. Based on those two examples, how is the angle ø in the formula related to the angle between the field and the normal direction?
 
  • #5


Hello, thank you for your question. The angle ø in this equation should be 60 degrees, since it is the angle between the normal vector and the direction of the electric field. Therefore, the electric flux through an equilateral triangle with side length 1m and a normal vector making 60 degrees with the electric field would be:

Φ = (8 N/C)(√3/4 m^2)cos(60 degrees) = 2√3 Nm^2/C
 

Related to Electric Flux of equilateral triangle

1. What is electric flux?

Electric flux is a measure of the electric field passing through a given surface. It is a scalar quantity and is measured in units of volts per meter (V/m).

2. How is electric flux calculated?

Electric flux is calculated by taking the dot product of the electric field vector and the surface area vector. This is represented by the equation Φ = E * A * cosθ, where E is the electric field, A is the surface area, and θ is the angle between the electric field and surface area vectors.

3. What is an equilateral triangle?

An equilateral triangle is a three-sided polygon with all three sides having equal length and all three angles measuring 60 degrees.

4. How does an equilateral triangle affect electric flux?

An equilateral triangle, as a geometric shape, does not have any inherent effect on electric flux. However, the electric flux passing through an equilateral triangle can be calculated using the aforementioned equation by considering the triangle's surface area and the electric field passing through it.

5. What are some real-world applications of electric flux of equilateral triangles?

One possible application of electric flux of equilateral triangles is in the design of electronic circuit boards. The equilateral triangular shape is commonly used in the layout of circuit boards to minimize the distance between components and reduce interference from external electric fields.

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