[Electrical force] Electrical charge in equilateral triangle

[sea333]

Homework Statement

In each corner of equilateral triangle there is a charge with 5 nAs. What force works on the e3 charge (see image). Length of a side is 5 cm. e1 is charged with negative charge.

Relevant Equations

F = (1/(4*Pi*eps0))*(e*e)/r^2

 

[PeroK]

Not being a computer myself, I find that a bit hard to follow! Can you explain what you're doing?

 

[sea333]

F23 is a force on the 3rd charge from 2nd charge
F13 is a force on the 3rd charge from the 1st charge
Fr is a sum of both (Pythagorean theorem).

 

[PeroK]

F23 is a force on the 3rd charge from 2nd charge
F13 is a force on the 3rd charge from the 1st charge
Fr is a sum of both (Pythagorean theorem).

Doesn't Pythagoras only apply to right-angled triangles?

 

[sea333]

Doesn't Pythagoras only apply to right-angled triangles?

I will check if forces are right-angled

 

[PeroK]

I will check this

There is a generalisation called the "rule of cosines", which is very useful.

 

[sea333]

There is a generalisation called the "rule of cosines", which is very useful.

I have used Cosines to calculate Fr and I still don't get the correct result:

 

[PeroK]

That's not right! Did you look up the rule of cosines?

 

[sea333]

Should I use the Law of cosines ? c^{2}=a^{2}+b^{2}-2ab*cos
Then I would need angle gamma?
I have updated the picture

 

[PeroK]

Yes. $\gamma$ can only be one thing!

 

[sea333]

I have used for gamma = 60 and got correct result but how do you know that gamma = 60 ?
I don't know why I thought that any of the angles is 90 degrees.
The correct result:

 

[sea333]

If you want to use Pythagorean theorem or Cos/Sin function you need one angle to be 90 degrees.

 

[PeroK]

how do you know that gamma = 60 ?

I looked at your diagram!