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1. Two small, identical spheres of mass m each are attached to thin light threads of length

a) If q

b) Draw a free-body diagram for either sphere, and hence find the distance x between the spheres in terms of q

F= kq

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[tex]\theta[/tex]/Sin[tex]\theta[/tex]' = 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 [tex]\theta[/tex] is. Any help would be greatly appreciated.

*L*each and hung from the same point. When charges q_{1}and q_{2}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 [tex]\theta[/tex] and [tex]\theta[/tex]' from the vertical.a) If q

_{1}= 3q_{2}, what is [tex]\theta[/tex]' in terms of [tex]\theta[/tex]? (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 q

_{1}, q_{2}, L, m, and any necessary physical constants. Assume that [tex]\theta[/tex] is small such that [tex]\theta[/tex] [tex]\approx[/tex] Sin[tex]\theta[/tex] [tex]\approx[/tex]Tan[tex]\theta[/tex]## Homework Equations

F= kq

_{1}q_{2}/d^{2}## 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[tex]\theta[/tex]/Sin[tex]\theta[/tex]' = 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 [tex]\theta[/tex] is. Any help would be greatly appreciated.

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