Coulomb's law — A negative charge balanced between 3 positive charges

[yesmale4]

Homework Statement

Three equal positive charges, q = 8.5 μC each, are arranged at the vertices of equilateral triangle (see figure below). A negative charge, Q, is placed at the center of the triangle such that all four charges are in equilibrium.

Relevant Equations

Ef=0
f=kq1q2/r^2

hello i would like to understand something, i found the right answer but there is still something i don't understand.
here is the figure

and here is my correct solution

what i don't understand is why F(3,Q) is 3kQ/r^2
i mean why is the 3? i only calculat the force between q3 and Q so why the 3 before?

 

[Steve4Physics]

You mean Coulomb's law. Not "colon law".

 

[yesmale4]

You mean Coulomb's law. Not "colon law".

fixed thank you

 

[kuruman]

Homework Statement:: Three equal positive charges, q = 8.5 μC each, are arranged at the vertices of equilateral triangle (see figure below). A negative charge, Q, is placed at the center of the triangle such that all four charges are in equilibrium.
Relevant Equations:: Ef=0
f=kq1q2/r^2

hello i would like to understand something, i found the right answer but there is still something i don't understand.
here is the figure
View attachment 316259

and here is my correct solution

View attachment 316260
View attachment 316261

what i don't understand is why F(3,Q) is 3kQ/r^2
i mean why is the 3? i only calculat the force between q3 and Q so why the 3 before?

What does r represent in your solution? The distance from where to where?

 

[BvU]

i found the right answer

What is the question ? (i can guess...)

I suppose

means $\sqrt{3}\over 2$ ?

You may want to learn some $\LaTeX$ (button at lower left of edit window). Or write and draw more unambiguously (the 60$^\circ$ at the lower left looks more like 45$^\circ$, smack between 30$^\circ$ and 60$^\circ$...)​

You seem to think that the sides of the triangle are $r$. Fine, but then the distance $qQ$ is not $r$ !

$\$

 

[Steve4Physics]

EDIT. Apologies @yesmale4. I misread your working. So this post is wrong and I've struck it through.

By the way @yesmale4, you have the incorrect unit in your answer. So your answer is wrong by a factor of one million!

Also, the value of q in the question is given to 2 significant figures. For consistency, your calculated value for Q should also have 2 significant figures.

 

[kuruman]

Also, the value of q in the question is given to 2 significant figures. For consistency, your calculated value for Q should also have 2 significant figures.

I don't see a calculated value. All I see is $Q=\dfrac{q}{\sqrt{3}}$ C. The issue is that there should be no units of Coulombs in the expression since it is a relation between magnitudes of charges.

 

[Steve4Physics]

I don't see a calculated value. All I see is $Q=\dfrac{q}{\sqrt{3}}$ C. The issue is that there should be no units of Coulombs in the expression since it is a relation between magnitudes of charges.

Whoops. In haste I misread $\frac q {\sqrt 3}$ as $\frac 9 {\sqrt 3}$ (though that would have been an incorrect answer in any case).

 

[SammyS]

Homework Statement:: Three equal positive charges, q = 8.5 μC each, are arranged at the vertices of equilateral triangle (see figure below). A negative charge, Q, is placed at the center of the triangle such that all four charges are in equilibrium.
Relevant Equations:: Ef=0
f=kq1q2/r^2

hello i would like to understand something, i found the right answer but there is still something i don't understand.
here is the figure
View attachment 316259

and here is my correct solution

[ ATTACH type="full" alt="aa.jpg"]316260[/ATTACH]
[ ATTACH type="full" alt="aaa.jpg"]316261[/ATTACH]

what I don't understand is why F(3,Q) is 3kQ/r^2
i mean why is the 3? i only calculated the force between q3 and Q so why the 3 before?

This seems rather strange. It's your solution, but you do not know where the 3 comes from.

Notice that the distance from q₁ to q₂ , etc. is not the same as the distance from each q to the central Q.

If you let R be the distance from each q to the charge Q in the center you should find that, $\dfrac{r/2}{R} =\cos(30^\circ)$ .

 

[haruspex]

It's your solution

Maybe not. Could be "found" as in "… in the back of the book".

Notice that the distance from q1 to q2 , etc. is not the same as the distance from each q to the central Q.

… and this is where the 3 comes from. $\frac 1{(\frac r{\sqrt 3})^2}=\frac 3{r^2}$