Two charged beads on a plastic ring

In summary, two charged beads are placed on a plastic ring, with one bead fixed at the origin and the other initially at 0 degrees on the x-axis. The bead on the x-axis is then moved to the opposite side, at 180 degrees, and the x and y components of the net electric field at the origin are plotted in Figures (b) and (c). Based on the given values for Ex and Ey, the charges of bead 1 and bead 2 are calculated to be 2.58E-12 C and -2.07E-12 C, respectively.
  • #1
kspabo
19
0

Homework Statement


Two charged beads are on the plastic ring in Figure (a). Bead 2, which is not shown, is fixed in place on the ring, which has radius R = 63.3 cm. Bead 1 is initially on the x axis at angle θ = 0o. It is then moved to the opposite side, at angle θ = 180o, through the first and second quadrants of the xy coordinate system. Figure (b) gives the x component of the net electric field produced at the origin by the two beads as a function of θ, and Figure (c) below gives the y component. The vertical axis scales are set by Exs = 5.80 × 104 N/C and Eys = -10.44 × 104N/C. (a) At what positive angle θ is bead 2 located? (Note: bead 2 is negative charged). What are the charges of (b) bead 1 and (c) bead 2?
W0473-N.jpg


Homework Equations


E = k (Q/R^2)

The Attempt at a Solution


[/B]
I understand Part 1. I realize that bead 2 must be located at +270 degrees. Because of this fact, we know that @180 degrees the only field acting on the origin in the X direction is from Bead 1. The same applies for the y-direction in @180 and 0 degrees with Q2 being the only field acting on it. So, for the Q1 I did as follows:@180

Ex = 5.8E4 = k (Q1/R^2)
Q1 = (5.8E4)(1/k)(R^2)
Q1 = (5.8E4)(1/8.99E9)(.633^2)
Q1 = 2.58E-6 C

For Q2
@0

Ey = 4 (-10.44E4 / 9) = -4.64E4 = k (Q2/R^2)
Q2 = (-4.64E4)(1/8.99E9)(.633^2)
Q2 = -2.07E-6 CWileyPlus is asking for it in uC so I just changed both from E-6 to E-12. I'm not getting the correct answer, where am I making a mistake? I'm starting to think this problem isn't as straightforward as I had assumed, although the solution I was given from the book is pretty much the same to as what I've done.
 
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  • #2
Your conversion is wrong.

You have for example ##Q_2 = -2.07 \times 10^{-6} C = -2.07 \mu C##.
 
  • #3
JorisL said:
Your conversion is wrong.

You have for example ##Q_2 = -2.07 \times 10^{-6} C = -2.07 \mu C##.
Wow I'm an idiot hah. For some reason I was doing the conversion wrong the 3 times I redid the problem. Thank you!
 

1. How do the charges on the beads affect each other?

The charges on the beads will either attract or repel each other, depending on their polarities. If the beads have opposite charges, they will attract each other. If they have the same charge, they will repel each other.

2. What happens if the charges on the beads are the same?

If the charges on the beads are the same, they will repel each other. This will cause the beads to move away from each other and potentially break the plastic ring if the repulsive force is strong enough.

3. Can the charges on the beads be changed?

Yes, the charges on the beads can be changed by rubbing them against a different material. This process, known as charging by friction, involves the transfer of electrons between the beads and the material, resulting in a change in their charges.

4. What role does the plastic ring play in this experiment?

The plastic ring serves as a medium for the beads to move around on. It also helps to keep the beads in a fixed position and prevents them from rolling off the surface. Additionally, the insulating properties of the plastic prevent the charges on the beads from dissipating.

5. How does the distance between the beads affect the strength of their interaction?

The strength of the interaction between the beads is directly proportional to the distance between them. As the distance between the beads increases, the force of attraction or repulsion decreases. This relationship follows the inverse square law, meaning that doubling the distance between the beads will result in a quarter of the original force.

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