Electrostatics: Calculating Charge on Suspended Spheres

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The discussion centers on calculating the charge on two small suspended spheres, each weighing 0.120g, which are 10.0cm apart due to electrostatic repulsion. The problem involves analyzing forces in static equilibrium, specifically the tension in the silk fibers (T1 and T2) and gravitational force (Fg). The tension components are crucial for determining the repulsive force, with the relationship F = Tx established for horizontal forces. The symmetry of the setup simplifies the analysis, allowing for a single tension value to be used for both spheres.

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Neerolyte
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two small spheres, each with 0.120g, have equal charges placed on them. Each sphere is suspended from the same point by its own silk fibre which are 75.0cm long. The repulsive force between them keep their centres 10.0cm apart. What is the charge on each sphere?
 
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It's a static equilibrium problem. Start by identifying all the forces acting on each sphere.
 
hm...this is what i think of it

Since there is strings involved, there must be tension. And since there are 2 strings connected to 1 point holding the 2 spheres. There must be T1 and T2. T1 and T2 must have components. We knew the mass of the two spheres so we know what Fg is, which equals to T1y and T2y.

Here is thing i don't know. Is T1x the repulsive force? IF it is, why does the data contain the string's length...and IF it is NOT, then I'm not sure how to do it...

yes i did a FBD, and identified all the forces. Fg, T, and repulsive force, that's it..
 
Neerolyte said:
Since there is strings involved, there must be tension. And since there are 2 strings connected to 1 point holding the 2 spheres. There must be T1 and T2. T1 and T2 must have components. We knew the mass of the two spheres so we know what Fg is, which equals to T1y and T2y.
Right. But the symmetry of the problem tells you that T = T1 = T2; you only need to deal with one of the two masses. And yes, the tension in the string exerts a force on the mass with components Tx and Ty. For equilibrium, Ty = mg.


Here is thing i don't know. Is T1x the repulsive force? IF it is, why does the data contain the string's length...and IF it is NOT, then I'm not sure how to do it...
The only forces acting horizontally are Tx and the repulsive force (F), so F = Tx. The length of the string and the distance between the masses will allow you to calculate the x and y components of the tension force. (Hint: One will be Tcos(theta); the other will be Tsin(theta).)

Next step: Rewrite the two force equations and solve for the repulsive force F.
 
yep got it ^_^

thank you very much
 

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