Solving an Electric Field Problem in Equilateral Triangle Geometry

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In summary, the conversation discusses the problem of finding the distance from a corner of an equilateral triangle to its center and from the midpoint of a baseline to the center. It involves using the Pythagorean theorem and trigonometric functions to find the correct measurements. The conversation also addresses a common misconception regarding the distance from the corner to the center.
  • #1
pyroknife
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This is from a electric field problem I'm trying to solve. This part I'm asking is geometry. I'm trying to find the distance from a corner of a equilateral triangle to its center. Also, I have to find the distance from the midpoint of a baseline to the center of the triangle.

Let's assume each side length is 2. Let's also assume that a corner lies at the top and the 2 other corners lie at the bottom like this pic http://upload.wikimedia.org/wikipedi...quilateral.svg . So I divide the triangle in half to find its height through the pythagorean theorem. 2^2-(2/2)^2=3. sqrt(3)=height. Then I divided the height by 2 and got .866 (using decimals cause idk how to type a square root symbol.) So wouldn't the .866 be the distance from the center to the midpoint of the baseline? Also, wouldn't it make it the distance from the top corner of the triangle to the center?? If that's the case doesn't that contradict the belief that all 3 corners have the same distance to the center of a equilateral triangle.

But when you calculate the distance from the corner to the center. You use the pythagorean thereom again. You have 1 for the base length and .866 for the height right? That gives you a hypotenuse of sqrt(1.75) which doesn't equal .866?

Can someone explain this to me please.
 
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  • #2
pyroknife said:
This is from a electric field problem I'm trying to solve. This part I'm asking is geometry. I'm trying to find the distance from a corner of a equilateral triangle to its center. Also, I have to find the distance from the midpoint of a baseline to the center of the triangle.

Let's assume each side length is 2. Let's also assume that a corner lies at the top and the 2 other corners lie at the bottom like this pic http://upload.wikimedia.org/wikipedi...quilateral.svg . So I divide the triangle in half to find its height through the pythagorean theorem. 2^2-(2/2)^2=3. sqrt(3)=height. Then I divided the height by 2 and got .866 (using decimals cause idk how to type a square root symbol.) So wouldn't the .866 be the distance from the center to the midpoint of the baseline? Also, wouldn't it make it the distance from the top corner of the triangle to the center?? If that's the case doesn't that contradict the belief that all 3 corners have the same distance to the center of a equilateral triangle.

But when you calculate the distance from the corner to the center. You use the pythagorean thereom again. You have 1 for the base length and .866 for the height right? That gives you a hypotenuse of sqrt(1.75) which doesn't equal .866?

Can someone explain this to me please.

You DO NOT divide height by 2 to find the distance to the center. The center lies along an angle bisector from each corner. Draw another triangle. Use trig.
 
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  • #3
Okay so the new triangle you draw. The hypotenuse goes from the corner to the center right? And the base would be 1 and the height would be .866? Also, is the midpoint of the base to the center .866 also
 
  • #4
[itex] sin(30°) = 1/2 [/itex]
[itex] cos(30°) = \frac{\sqrt{3}}{2}[/itex]

In a 30-60-90 triangle (angles), the sides have relationships 1 - 2 - [itex]\sqrt{3}[/itex], where side of relative length 2 is on the hypotenuse.

attachment.php?attachmentid=38397&stc=1&d=1314676804.gif
 

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  • #5
pyroknife said:
Okay so the new triangle you draw. The hypotenuse goes from the corner to the center right? And the base would be 1 and the height would be .866? Also, is the midpoint of the base to the center .866 also

The base would be 1 and the vertex angle would be pi/6, right? That doesn't make the height sqrt(3)/2. It's different.
 
  • #6
After looking at gneill's picture please say you know the height isn't .866. FAST. You seem to be stuck on that.
 

1. How do I determine the direction of the electric field at a point in an equilateral triangle geometry?

The direction of the electric field at a point in an equilateral triangle geometry can be determined by using the right hand rule. Simply point your thumb in the direction of the electric field and curl your fingers in the direction of the electric force. The direction of your fingers represents the direction of the electric field.

2. What is the relationship between the distance from the charge and the electric field strength in an equilateral triangle geometry?

The electric field strength in an equilateral triangle geometry is directly proportional to the distance from the charge. This means that the farther away you are from the charge, the weaker the electric field will be. Similarly, the closer you are to the charge, the stronger the electric field will be.

3. How do I calculate the magnitude of the electric field at a point in an equilateral triangle geometry?

The magnitude of the electric field at a point in an equilateral triangle geometry can be calculated using the formula E = kQ/r^2, where k is the Coulomb's constant, Q is the magnitude of the charge, and r is the distance from the charge to the point. Make sure to use consistent units when plugging in values for the formula.

4. Can the electric field in an equilateral triangle geometry be zero?

Yes, the electric field in an equilateral triangle geometry can be zero at certain points. This occurs when there are equal and opposite charges located at the vertices of the triangle. The electric fields from each charge cancel each other out at the center of the triangle, resulting in a net electric field of zero.

5. How does the shape of an equilateral triangle affect the electric field?

The shape of an equilateral triangle does not have a significant impact on the electric field. The magnitude and direction of the electric field are determined by the distance from the charge and the charge itself, rather than the shape of the triangle. However, the placement of the charge within the triangle can affect the direction and magnitude of the electric field at different points.

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