Electric Field of Point Charges in Equilateral Triangle

In summary: That is what much of the math is about.You need to be able to check your own work, else you will never know if you are right.
  • #1

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Homework Statement


A point charge [itex]q =+6.4 \mu \mathrm{C}[/itex] is placed at each corner of an equilateral triangle with sides [itex]0.29 \mathrm{m}[/itex] in length.
What is the magnitude of the electric field at the midpoint of any of the three sides of the triangle?

Hint: if you are careful to examine the symmetry of this problem before starting to calculate, you will notice that the problem is much shorter than you think!

Homework Equations



$$E=\frac{kq}{r^2}$$

The Attempt at a Solution


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I suspect that the hint alludes to the fact that at the midpoint of any given side, the electric field of the two adjacent charges whose position lie along the same axis as the midpoint will in effect cancel each other out. Therefore, the only electric field I need to calculate is that of the point charge furthest from the midpoint of that given side.

I know the charge [itex]q =+6.4\times 10^{-6} \mathrm{C}[/itex] and that the distance [itex]r[/itex] between the point charge and midpoint is the height of the equilateral triangle so that [itex]r=\frac{\sqrt{3}}{2}\times.29\mathrm{m}[/itex].

If I plug these into the equation, I get
$$E=k\frac{6.4\times 10^{-6} \mathrm{C}}{(\frac{\sqrt{3}}{2}\times.29\mathrm{m})^2}$$
$$=
\boxed{911935.4964~ \mathrm{N/C}}$$

Is this the correct answer?

Thank you.
 
Last edited:
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  • #2
The reasoning is sound ... havn't checked the arithmetic.
 
  • #3
Thank you for your feedback, Simon! The answer I posted was indeed correct.
 
  • #4
Well done.

Just a note:
I may have said that the answer was right or wrong fersure, but how do you know I got it right?
You are training to work on problems where nobody knows the right answer, so there is nobody to ask.
As you progress you need to start thinking about how you can tell that you have it right without having to ask someone.
 

1. What is an equilateral triangle and how does it relate to electric fields?

An equilateral triangle is a shape with three equal sides and three equal angles. In the context of electric fields, an equilateral triangle can represent the arrangement of three point charges with equal magnitude and opposite signs, creating a symmetrical electric field.

2. How do I calculate the electric field at a point in an equilateral triangle?

To calculate the electric field at a point in an equilateral triangle, you can use the superposition principle and the formula for the electric field of a point charge. Simply calculate the electric field of each individual point charge at the given point and then add them together vectorially.

3. Why are point charges used in the study of electric fields in an equilateral triangle?

Point charges are used in the study of electric fields in an equilateral triangle because they represent a simplified and idealized version of real-world systems. They allow for easier calculations and analysis of the electric field in a triangular arrangement.

4. What is the relationship between the distance and strength of the electric field in an equilateral triangle?

The electric field strength at a point in an equilateral triangle is inversely proportional to the distance from that point to the charges. As the distance increases, the strength of the electric field decreases. This relationship is described by the inverse square law.

5. How does the direction of the electric field vary in an equilateral triangle?

In an equilateral triangle with three equal point charges, the direction of the electric field will be the same at all points within the triangle. This is because the electric field lines will be symmetrical and point away from the positive charges and towards the negative charges, creating a balanced and uniform field.

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