What Potential Difference Causes a Charged Sphere to Tilt 30 Degrees?

[jaredmt]

Homework Statement

A small sphere with mass .015kg hangs by a thread between two parallel vertical plates .05m apart. The plates are insulating and have a uniform surface charge densities +σ and -σ. The charge on the sphere is q = 8.9 x 10^-6 C. What potential difference between the plates will cause the thread to assume an angle of 30 degrees with the vertical?

Homework Equations

some formulas in the chapter and on a previous chapter. I am not sure which ones are useful:
dV = -Edl
Ua - Ub = q(Va - Vb)
Kb = Ka + Ua - Ub
Kb = .5mv^2
Va - Vb = Ed
F = qE
p = qd
Torque = pEsinθ
Torque = p X E

The Attempt at a Solution

I am clueless. the only thing i know is Ka = 0 because it started at rest. that means Kb/q = Va - Vb
but then again the velocity at Kb would = 0 wouldn't it? so I don't know. do I find the F by figuring out E somehow? or does it have something to do with Torque? i don't know how to find p (electric dipole moment). so yea I am lost, any help would be appreciated

I think it has something to do with the gravity pulling down then the E pulling/pushing to the side.

 

[Doc Al]

Think of this as a statics problem, where one of the forces is the electric force. What forces act on the sphere? What is the net force?

 

[jaredmt]

Think of this as a statics problem, where one of the forces is the electric force. What forces act on the sphere? What is the net force?

ok so does that mean F = qE is pushing to the side and gravity pushing down?

edit: o wait. Va - Vb = Ed.

the equation of E i believe is this: E = qσ/2πε(.025^2)
we have all that accept σ. d is just .025m (correct me if I am wrong on any of this).

then i guess you use F = qE + gravitational force and set the angle to 30 degrees, then solve for σ. then plug that into Ed to get the answer of Va - Vb right?

somethign isn't right, I am not coming out with the right answer :(

 

[jaredmt]

ok how can i find net force? and is E = qσ/2πε(.025^2) the correct equation for E?

i did E = qσ/4πε(.025^2) + qσ/4πε(.025^2) = qσ/2πε(.025^2)

 

[Doc Al]

ok so does that mean F = qE is pushing to the side and gravity pushing down?

Yes. Don't forget the string tension.

edit: o wait. Va - Vb = Ed.

You'll need that.

the equation of E i believe is this: E = qσ/2πε(.025^2)
we have all that accept σ. d is just .025m (correct me if I am wrong on any of this).

You won't need that to answer the question.

then i guess you use F = qE + gravitational force and set the angle to 30 degrees, then solve for σ. then plug that into Ed to get the answer of Va - Vb right?

The first thing to do is to solve for the electric force on the sphere, using statics. Once you have the force, you can figure out the field needed and then the potential difference.

ok how can i find net force? and is E = qσ/2πε(.025^2) the correct equation for E?

i did E = qσ/4πε(.025^2) + qσ/4πε(.025^2) = qσ/2πε(.025^2)

You don't need any equation that contains σ.