E&M Problem - 2 Charged Masses Hanging on Strings

AI Thread Summary
The problem involves two charged masses hanging from strings, one with charge q and the other with charge 2q, and requires finding the angles they make with the vertical. The electric forces acting on each charge are equal and opposite, while gravity also influences their positions. The tension in the strings can be analyzed using three equations that relate tension, the angle from the vertical, and the horizontal distances of each mass. The discussion highlights the challenge of incorporating mass and charge into the calculations to derive the angles. Ultimately, the goal is to solve for the angles θ using the established relationships.
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E&M Problem -- 2 Charged Masses Hanging on Strings

Homework Statement



Two charges of identical mass m, one with charge q, the other with charge 2q, hang from strings
of length l from a common point. Assume q is sufficiently weak so that any angle you're looking
for is very small, and find an approximate expression for the angle  each charge makes with
respect to the vertical. Check (and show) that the units work out, and that the limiting behavior
for large mass, large length, and/or small q are at least sensible.


Homework Equations


Coulombs Law
E=(1/4*pi*episolon)(q' R/R)


The Attempt at a Solution



First I am not sure what to do with the mass, if its really even needed.
Also I am given lengths, but it doesn't specify that they are the vectors themselves, otherwise I would just use the r' vector to the charge and the r vector to some random point charge in the middle to grab the vertical angle.

I think there is another way I am missing though. Any help or insight would be appreciated.
 
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First think about which forces are acting on the charged masses. Then your electric field of a charge Q in the origin should read (in SI units)
\vec{E}=\frac{Q}{4 \pi \epsilon_0} \frac{\vec{r}}{r^3}.
 
vanhees71 said:
First think about which forces are acting on the charged masses. Then your electric field of a charge Q in the origin should read (in SI units)
\vec{E}=\frac{Q}{4 \pi \epsilon_0} \frac{\vec{r}}{r^3}.


So there will be a bigger force acting upon q as opposed to 2q. The angle between the vertical and q will be bigger than the other. I guess I am having trouble relating that into the formula, or even figuring out how to get the angles out of it. I am sorry for the huge mind block that I am experiencing
 
inferno298 said:
So there will be a bigger force acting upon q as opposed to 2q. The angle between the vertical and q will be bigger than the other. I guess I am having trouble relating that into the formula, or even figuring out how to get the angles out of it. I am sorry for the huge mind block that I am experiencing

The electrostatic forces on the two masses are equal & opposite. They're in the x direction.

Remember that gravity also acts on both of them. Equal forces here too. In the y direction.

So the two masses hang the same angle from the vertical.

Call the tension in each string = T
Then write 3 equations relating T, the angle from the vertical θ, and the distance eack mass assumes horizontally from the at-rest (zero electrostatic forces) position.

3 equations, 3 unknowns. Solve for θ.
 
Last edited:
alright thanks, I almost got it now
 
Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
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