Two tiny spheres of mass = 7.20 mg carry charges of equal magnitude, 72.0 nC , but opposite sign. They are tied to the same ceiling hook by light strings of length 0.530 m . When a horizontal uniform electric field E that is directed to the left is turned on, the spheres hang at rest with the angle between the strings equal to 50.0 degrees.
What is the magnitude E of the field?
Fe1 = Eq
Fe2 = (Kq1q2)/r2
Fg = mg
The Attempt at a Solution
I assumed that the state it is in is in equilibrium so I set up:
ƩF = Fg + Fe1 + Fe2 + T = 0
ƩTx = Tcosθ - Fe1 + Fe2 = 0
θ being 65 degrees since I split the triangle made by the 50 degrees into 2 right triangles.
ƩTy = Tsinθ - mg = 0
T = (Fe1 - Fe2)/cosθ
Ty = (Fe1 - Fe2)tanθ - mg = 0
Fe1 = mg/tanθ + Fe2
E = (mg/tanθ + kq1q2/r2)/q
(I found r to be .448 using the right triangles I formed)
I plugged in all the given values and I've got...1.17 x 10^6
Which is wrong. Can someone please explain what I messed up on?