Determine the magnitude of the force on each charge

[meme177]

1. The problem

Two negative and two positive point charges (magnitude Q = 3.16mC ) are placed on opposite corners of a square (side lengths a = 0.105m )

#1. Determine the magnitude of the force on each charge.

I GOT... F1,F2,F3,F4 =7.44x10^6N (which was marked correct)

I am having trouble with this question...

#2. Determine the direction of the force on each charge.
I know (Fy/Fx)=1
so tan-1(1)=45

Its asking for θ1,θ2,θ3,θ4 and I have no idea how to get the angles :(

 

[BvU]

Hello meme, and welcome to PF.

If you know the tangent, you know the angle (plus or minus pi), isn't it ?
However, the "I know (Fy/Fx)=1" applies to which of the charges, exactly ? How about the other three ?

And: have you altready defined what theta is ? Or was it given ?

 

[meme177]

θ1,θ2,θ3,θ4
I have tried these answers (in order)
225,225,225,225=WRONG (but then I was like NO this is impossible)
Then I tried
135,45,315,225=WRONG

I don't know what to do anymore

 

[BvU]

the "I know (Fy/Fx)=1" applies to which of the charges, exactly ?
It can surely not apply to all four of them !

 

[meme177]

Charge #2 where I calculated the y and x component of the force for question #1

 

[meme177]

I think I see it! charge #2 is 45 ...Charge#1 (45+90=135)...charge#4 (180+45=225)...charge#3 (45+90=135) ??

 

[BvU]

Still a small matter of signs: my hunch for e.g. #2 is that two attracting forces from charges closer by overcome one repelling force from #4. From there, with symmetry considerations, all forces are towards the center of the square. Agree ?

 

[meme177]

okay, I agree.

 

[meme177]

with the forces all pointing to the middle, they cancel (no movement)
Now I have θ1= -45 θ2= -135 θ3= 45 θ4=135
Is this correct, now?

 

[BvU]

So theta is the angle wrt the positive x-axis.
I think you swapped 3 and 4 (in your post not in the drawing)
Movement doesn't apply here. The charges are positioned in fixed given places,
and there is no mention of how they are kept there...

 

[meme177]

Yes, so θ1= -45, θ2= -135, θ3= 135, θ4=45 ? Am I doing the angles wrt positive x-axis right?

 

[BvU]

Yes and yes, IMHO.

 

[SammyS]

with the forces all pointing to the middle, they cancel (no movement)
Now I have θ1= -45 θ2= -135 θ3= 45 θ4=135
Is this correct, now?

Do like charges attract, or do they repel?

 

[BvU]

@Sam: Meme is talking about the net forces, I should think. The magnitude was already calculated in part #1 of post #1.

 

[SammyS]

@Sam: Meme is talking about the net forces, I should think. The magnitude was already calculated in part #1 of post #1.

Okey-Dokey .

 

[meme177]

Mastering Physics is still counting the angles wrong :/

 

[SammyS]

Mastering Physics is still counting the angles wrong :/

Does M P want radians?

Otherwise M P may want you to specifically say, degrees, or ° .

 

[meme177]

no, the units are already there (degrees) counterclockwise from the +x axis

 

[meme177]

Here is how it looks

 

[SammyS]

Maybe they want

θ₁, θ₂, θ₃, θ₄ =

315, 225, 135, 45

but I see you have only 2 tries remaining.

 

[meme177]

I got it! ... thanks guys!

 

[SammyS]

I got it! ... thanks guys!

That's good to hear.

M P really should have taken your answers with the negative angles. They give exactly the same orientation for the vectors.

 

[BvU]

Goes to show programmers and teachers are different, both only human.
Well done, meme and thanks for helping out, Sam.

M P should do something about this. All the physics was already in part A and part B is more like a detective to find out what their limited answer domain is.