Determine the magnitude of the force on each charge

In summary, the problem involves four point charges, two negative and two positive, placed on opposite corners of a square. The magnitude of the force on each charge is determined to be 7.44x10^6N, with a side length of 0.105m. The direction of the force on each charge is calculated to be -45° for θ1, -135° for θ2, 135° for θ3, and 45° for θ4. However, it is noted that the answers may also be accepted as 315°, 225°, 135°, and 45°, with the negative angles representing the same orientation as the positive angles.
  • #1
meme177
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0
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 :(
 

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  • #2
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 ?
 
  • #3
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
 
  • #4
the "I know (Fy/Fx)=1" applies to which of the charges, exactly ?
It can surely not apply to all four of them !
 
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  • #5
Charge #2 where I calculated the y and x component of the force for question #1
 
  • #6
I think I see it! charge #2 is 45 ...Charge#1 (45+90=135)...charge#4 (180+45=225)...charge#3 (45+90=135) ??
 
  • #7
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 ?
 
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  • #8
okay, I agree.
 
  • #9
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?
 

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  • #10
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...
 
  • #11
Yes, so θ1= -45, θ2= -135, θ3= 135, θ4=45 ? Am I doing the angles wrt positive x-axis right?
 
  • #12
Yes and yes, IMHO.
 
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  • #13
meme177 said:
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?
 
  • #14
@Sam: Meme is talking about the net forces, I should think. The magnitude was already calculated in part #1 of post #1.
 
  • #15
BvU said:
@Sam: Meme is talking about the net forces, I should think. The magnitude was already calculated in part #1 of post #1.
Okey-Dokey .
 
  • #16
Mastering Physics is still counting the angles wrong :/
 
  • #17
meme177 said:
Mastering Physics is still counting the angles wrong :/
Does M P want radians?

Otherwise M P may want you to specifically say, degrees, or ° .
 
  • #18
no, the units are already there (degrees) counterclockwise from the +x axis
 
  • #19
Here is how it looks
 

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  • #20
Maybe they want

θ1, θ2, θ3, θ4 =

315, 225, 135, 45

but I see you have only 2 tries remaining.
 
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  • #21
I got it! ... thanks guys!
 

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  • #22
meme177 said:
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.
 
  • #23
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.
 

What is the formula for calculating the magnitude of force on each charge?

The formula for calculating the magnitude of force on each charge is F = k * (q1 * q2) / r^2, where F is the force, k is the Coulomb's constant, q1 and q2 are the charges, and r is the distance between the two charges.

How do you determine the direction of the force on each charge?

The direction of the force on each charge can be determined by using the principle of superposition. This means that the force on a charge is the vector sum of the forces from all other charges. The direction of the force is in the direction of the resulting vector.

What are the units for the magnitude of force on each charge?

The units for the magnitude of force on each charge are Newtons (N). This is the unit for force in the International System of Units (SI).

How does the distance between the charges affect the magnitude of force?

The magnitude of force between two charges is inversely proportional to the square of the distance between them. This means that as the distance increases, the force decreases and vice versa.

Can the magnitude of force on each charge be negative?

Yes, the magnitude of force on each charge can be negative. This occurs when the two charges have opposite signs (one positive and one negative), resulting in an attractive force between them. A positive value indicates repulsion between two charges with the same sign.

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