Point charges in a equilateral triangle - typo in solution?

In summary: The magnitude of the force is the product of the charges and the force, so it will be 3.0 µC for each charge.
  • #1
chopnhack
53
3

Homework Statement


Three point charges each carrying a charge of 11.0 µC are located at the corners of an equilateral triangle of side 15.0 cm. Calculate the magnitude and direction of the force on each charge.

Homework Equations


k = 9.0x109NM2C-2
F = k⋅(Q1⋅Q2)/r2

The Attempt at a Solution


See attached. My main problem lies with the solution provided which shows on ii) the solution for the left vertex as arctan of 41.9/72.6 whereas I got 72.6/41.9 as in tan = opp/adj. Is it a typo or have I totally missed the mark?
hw1q5.jpg
Lesson 2.1 Homework Solutions_Page_2.jpg

Lesson 2.1 Homework Solutions_Page_3.jpg
 
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  • #2
Isn't it easier to find the force on charge 2 first, and then use that to get the magnitude and direction of the forces on charges 1 and 3?
 
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  • #3
Hard to read, your writing is...
However, I think you could see from symmetry alone that the 30 degree angle (or 210, if you want), is correct. Not 240 !

Your division finds the angle between the y-axis and the force; we are used to reporting the angle between the force and the postiive x-axis...
 
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  • #4
Chestermiller said:
Isn't it easier to find the force on charge 2 first, and then use that to get the magnitude and direction of the forces on charges 1 and 3?
Hi Chester! I honestly picked the first vertex and went to work. Being that they are all equal charges, I didn't see the difference in locations.
Can you comment on my tan theta question?

Thanks as always.
 
  • #5
BvU said:
Hard to read, your writing is...
However, I think you could see from symmetry alone that the 30 degree angle (or 210, if you want), is correct. Not 240 !

Your division finds the angle between the y-axis and the force; we are used to reporting the angle between the force and the postiive x-axis...

Sorry about that! The work was to only be for internal use and discarded, practice to understand the application - I literally have a dozen more of these to do before I will feel comfortable moving on to the next chapter and they each take quite a bit of time... so fast and sloppy it is!

I think I see what you mean, I believe that my force diagram is misdrawn... what I have labelled resultant in yellow is actually the extension of the force between 2 and 1... and the erased green line was correct - the resultant would have been drawn somewhere between them!

I am still having trouble visualizing the proper placement of the vectors to give me tan 41/72 though...

Thanks
 
  • #6
Thanks all - I had to redraw to see it. Thank you again.
 
  • #7
chopnhack said:
Hi Chester! I honestly picked the first vertex and went to work. Being that they are all equal charges, I didn't see the difference in locations.
Can you comment on my tan theta question?

Thanks as always.
I'm too lazy to look at that, since the problem is so much easier if the focus is on charge 2. For the other two charges, the direction will be the bisector of the included angle; that will be at an angle of 30 degrees to each of the two sides.
 

Related to Point charges in a equilateral triangle - typo in solution?

1. What is a point charge?

A point charge is a hypothetical, infinitesimally small electric charge that is used in physics to simplify calculations and models. It is a fundamental concept in electrostatics, and is denoted by the letter "q".

2. What is an equilateral triangle?

An equilateral triangle is a geometric shape with three sides of equal length and three angles of 60 degrees each. It is a special case of a regular polygon and has several unique properties, including symmetry and equal angles between its sides.

3. What is the significance of point charges in an equilateral triangle?

In an equilateral triangle, the three point charges are at equal distances from each other and form a symmetrical pattern. This can have implications for the electric field and potential energy at each point, and can help in solving problems involving electric charges and their interactions.

4. What is the typo in the solution?

The typo in the solution may refer to an error or mistake in the calculations, equations, or assumptions made in solving the problem involving point charges in an equilateral triangle. It could also refer to a misspelling or incorrect use of units or symbols.

5. How can I correct the typo in the solution?

To correct the typo in the solution, you can carefully review the calculations and equations used, check for any incorrect assumptions or units, and make necessary adjustments. If you are unsure, you can consult with a colleague or refer to reliable sources for guidance.

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