How do I find Q without having a distance r?

  • Thread starter BuBbLeS01
  • Start date
In summary, We are given the thread length and angle to find the charge q for two equally charged point masses that repel each other. By setting up two equations for the horizontal and vertical forces and rearranging to solve for q, we get the equation q = (mg*tanθ) / (kq/r^2) which can be simplified to q = (mgr^2*tanθ) / k.
  • #1
BuBbLeS01
602
0
Charges...please help!

Homework Statement



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Two 3.52 g point charges on 7.49-m-long threads repel each other after being equally charged. What is the charge q? (θ=31°.)


Homework Equations


F = KQQ/R^2


The Attempt at a Solution


How do I find Q without having a distance r?
 
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  • #2
BuBbLeS01 said:
How do I find Q without having a distance r?
You are given the thread length and the angle--use that to figure out the distance.
 
  • #3
Oh yea...so the length from the center to one of the masses is 3.858 m.
So I can do...
F = K*Q*Q/r^2
F = K*Q^2/ r^2
An wouldn't F = 0 since they cancel each other out?
 
  • #4
Since the masses are in equilibrium, the net force on each is zero. What forces act on each mass?
 
  • #5
Tension
 
  • #6
BuBbLeS01 said:
Tension
That's one force. List them all. (And draw yourself a free body diagram showing how the force act on each mass.)
 
  • #7
Tension and weight are the forces
 
  • #8
So do I include the electric force? Like...
T - W + Fel = 0
 
  • #9
BuBbLeS01 said:
Tension and weight are the forces
Don't forget the electrostatic force!
 
  • #10
Isn't that Fel?
 
  • #11
BuBbLeS01 said:
So do I include the electric force? Like...
T - W + Fel = 0
Yes, but realize that forces are vectors--direction counts. Set up two equations: One for the horizontal components, one for the vertical components. Combine these to solve for the charge.
 
  • #12
X.) TSINθ + qE = 0
y.) TCOSθ - mg = 0

T = mg/COSθ
mg/COSθ * SINθ + qE
q = -mg*TANθ/E
 
  • #13
BuBbLeS01 said:
X.) TSINθ + qE = 0
y.) TCOSθ - mg = 0
I'd write that first equation as:
Tsinθ - qE = 0 (since the force components are in opposite directions)

Realize that E is also a function of q, so rewrite that in terms of k, q, and r (which you figured out).

Otherwise, you are on the right track.
 
  • #14
Okay so I end up with...
-q = -(mg*tanθ) / (kq/r^2)
q = (mg*tanθ) / (kq/r^2)
and the q's cancel?
= (mg*tanθ) / (k/r^2)
 
  • #15
BuBbLeS01 said:
Okay so I end up with...
-q = -(mg*tanθ) / (kq/r^2)
q = (mg*tanθ) / (kq/r^2)
and the q's cancel?
The q's don't cancel. And when you divide by a fraction, simplify the result. (Invert and multiply.)
 

1. How do I find Q if I don't know the distance r?

To find Q without knowing the distance r, you can use the equation Q = k(Q1*Q2)/r^2, where k is the Coulomb's constant, Q1 and Q2 are the charges involved, and r is the distance between them. If you don't know the value of r, you can use other known quantities, such as the force between the charges or the electric field, to solve for Q.

2. Can I find Q using only one charge and the electric field?

Yes, you can find Q using only one charge and the electric field. The electric field can be calculated using the equation E = k(Q/r^2), where k is the Coulomb's constant, Q is the charge, and r is the distance between the charge and the point where the electric field is being measured. By rearranging this equation, you can solve for Q if you know the value of the electric field and the distance r.

3. Is it possible to find Q without knowing the charges involved?

No, it is not possible to find Q without knowing the charges involved. The equation Q = k(Q1*Q2)/r^2 involves two charges, Q1 and Q2. If you don't know the values of these charges, you cannot accurately calculate the value of Q.

4. Can I find Q using the electric potential instead of the electric field?

Yes, you can find Q using the electric potential. The electric potential can be calculated using the equation V = k(Q/r), where k is the Coulomb's constant, Q is the charge, and r is the distance between the charge and the point where the potential is being measured. By rearranging this equation, you can solve for Q if you know the value of the electric potential and the distance r.

5. Is there a way to find Q without using any equations?

No, there is no way to find Q without using any equations. The concept of electric charge and its effects on other charges and fields is based on mathematical principles and cannot be determined without using equations. However, there are calculators and online tools available that can help you easily solve these equations and find the value of Q.

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