Two unequal charges repel, suspended from same point.

[Darkwolf312]

1. Two small, identical spheres of mass m each are attached to thin light threads of length L each and hung from the same point. When charges q₁ and q₂ are placed on upon the spheres(with both charges having the same sign), the two spheres repel each other and, upon reaching equilibrium, hang at angles $$\theta$$ and $$\theta$$' from the vertical.
a) If q₁= 3q₂, what is $$\theta$$' in terms of $$\theta$$? (Hint: Consider Newton's Third Law)
b) Draw a free-body diagram for either sphere, and hence find the distance x between the spheres in terms of q₁, q₂, L, m, and any necessary physical constants. Assume that $$\theta$$ is small such that $$\theta$$ $$\approx$$ Sin$$\theta$$ $$\approx$$Tan$$\theta$$

Homework Equations

F= kq₁q₂/d²

The Attempt at a Solution

In my first attempt at the problem, I assumed the forces caused by the charges were perpendicular to the vertical and thus got the answer Sin$$\theta$$/Sin$$\theta$$' = 1. I think this answer is incorrect, but I got it by equating the two forces caused by the charges, and hence equating the x-component of the two tension forces.

I guess the correct way to do it would be to take the electrostatic forces as being in line with the distance, but I can't seem to figure out the angle between the force and the horizontal. I am also unsure as to whether I should use the statement given in part b as how small $$\theta$$ is. Any help would be greatly appreciated.

 

[tiny-tim]

Welcome to PF!

Hi Darkwolf312! Welcome to PF!

(have a theta: θ )

Assume that $$\theta$$ is small such that $$\theta$$ $$\approx$$ Sin$$\theta$$ $$\approx$$Tan$$\theta$$
…
In my first attempt at the problem, I assumed the forces caused by the charges were perpendicular to the vertical and thus got the answer Sin$$\theta$$/Sin$$\theta$$' = 1. I think this answer is incorrect, but I got it by equating the two forces caused by the charges, and hence equating the x-component of the two tension forces.

I guess the correct way to do it would be to take the electrostatic forces as being in line with the distance, but I can't seem to figure out the angle between the force and the horizontal.

Yes, you're correct, the force is in line with the distance …

but you should assume that the charges are at the same level, so that the forces are horizontal …

that's what the question is trying to get at when it talks about θ being small!