# E&M Problem - 2 Charged Masses Hanging on Strings

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 im not sure what to do with the mass, if its really even needed.
Also im 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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vanhees71
Gold Member
2019 Award
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)
$$\vec{E}=\frac{Q}{4 \pi \epsilon_0} \frac{\vec{r}}{r^3}.$$

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. Im sorry for the huge mind block that I am experiencing

rude man
Homework Helper
Gold Member
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. Im 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.

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alright thanks, I almost got it now