Physics-Electric Fields: Can someone please explain this to me?

[MitsuShai]

My professor didn't explain this well.

Question: http://i324.photobucket.com/albums/k327/ProtoGirlEXE/q1.jpg


Answer: (part 1) http://i324.photobucket.com/albums/k327/ProtoGirlEXE/q2.jpg
(part 2) http://i324.photobucket.com/albums/k327/ProtoGirlEXE/q3.jpg


I'm completely lost on this one. I don't understand how this problem was solved.

So I'm guessing q4 is the point where you measure the forces from the other 3 points. But I thought that q3 won't have a y value and q1 won't have an x value.
So q2 is only measured by the diagonal right? So it would just be F= k Q^2/(2L^2)---I understand this

why wouldn't q1 and q3 just be F=k Q^2/L^2?

I would like it if someone would explain this whole problem because I feel like I'm completely lost on it.

 

[tiny-tim]

Hi MitsuShai!

(try using the X² and X₂ icons just above the Reply box )

… But I thought that q3 won't have a y value and q1 won't have an x value.
So q2 is only measured by the diagonal right? So it would just be F= k Q^2/(2L^2)---I understand this

why wouldn't q1 and q3 just be F=k Q^2/L^2?

They are.

I think you're confused about what the x and y coordinates are.

Your professor has looked at the diagram, and decided that it's obvious that the total force will be along the diagonal …

and so he's decided to make his x coordinate in that direction (instead of along the bottom of the square, as you'd expect).

Does his work make sense now? ​

 

[MitsuShai]

Hi MitsuShai!

(try using the X² and X₂ icons just above the Reply box )


They are.

I think you're confused about what the x and y coordinates are.

Your professor has looked at the diagram, and decided that it's obvious that the total force will be along the diagonal …

and so he's decided to make his x coordinate in that direction (instead of along the bottom of the square, as you'd expect).

Does his work make sense now? ​

Oh ok I think I know what you mean. The forces are the diagonal [F= k Q[SUP]2[/SUP]/(2L²)] and the x and y components of the diagonal, which are F=k Q²/L² each.
And to get the total forces, you have to add up these forces, but the answer is suppose to be [Q²/(8pi*epsilon_0*L²)] (1+2sqrt(2)) and you don't get that with these forces...

 

[tiny-tim]

Hi MitsuShai!

(have a square-root: √ and an epsilon: √ and a pi: π )

And to get the total forces, you have to add up these forces, but the answer is suppose to be [Q²/(8pi*epsilon_0*L²)] (1+2sqrt(2)) and you don't get that with these forces...

Show us what you get.

(btw, I've just noticed i should have said "y" not "x" in my last post )

 

[MitsuShai]

Hi MitsuShai!

(have a square-root: √ and an epsilon: √ and a pi: π )Show us what you get.

(btw, I've just noticed i should have said "y" not "x" in my last post )

F(total)= [ k Q²/(2L²)] + [ k Q²/(L²)] + [ k Q²/(L²)] = [ k Q²/(2L²)] + [2k Q²/(L²)]= [ k Q²/(2L²)] + [4k Q2/(2L²)]= 5k Q²/(2L²)= 3k Q²/(L²)

 

[tiny-tim]

Hi MitsuShai!

(just got up :zzz: …)

F(total)= [ k Q²/(2L²)] + [ k Q²/(L²)] + [ k Q²/(L²)] = [ k Q²/(2L²)] + [2k Q²/(L²)]= [ k Q²/(2L²)] + [4k Q2/(2L²)]= 5k Q²/(2L²)= 3k Q²/(L²)

ah I see …

no, you need to use the component of F₁ and F₃ along the diagonal, not the whole of F₁ and F₃ …

try again! ​

 

[MitsuShai]

Hi MitsuShai!

(just got up :zzz: …)ah I see …

no, you need to use the component of F₁ and F₃ along the diagonal, not the whole of F₁ and F₃ …

try again! ​

Oh right, I forgot about that part, so
F(total)= [ k Q^2/(2L^2)] + [ k Q^2/(L^2)]sin(45) + [ k Q^2/(L^2)]cos(45)= 2[ k Q^2/(L^2)](1/sqrt(2)) + [ k Q^2/(2L^2)]= [ k Q^2/(2L^2)](1/sqrt(2)) + 4k Q^2/(2L^2)][1/sqrt(2)/(1/sqrt(2)] I'm doing this wrong, somehow... :/

 

[tiny-tim]

Hi MitsuShai!

(please use the X² icon just above the Reply box )

2[ k Q^2/(L^2)](1/sqrt(2)) + [ k Q^2/(2L^2)]

that's correct …

i can't see where you've gone wrong after that

 

[MitsuShai]

Hi MitsuShai!

(please use the X² icon just above the Reply box )


that's correct …

i can't see where you've gone wrong after that

Where do I go from there? I was thinking of adding them and to do that I would need to have common denominators, so I would have to get common denominators and I just noticed that I typed that in wrong... ._.

2[ k Q^2/(L^2)](1/sqrt(2)) + [ k Q^2/(2L^2)]= [ k Q^2/(2L^2)](1/sqrt(2)) + 4k Q^2/(2L^2)](1/sqrt(2))= 5k Q^2/(4L^2), which isn't right