Electric Field and a Charged Cork Ball on a Massless String

[gsquare567]

Homework Statement

A charged cork ball of mass 1g is suspended on a light string in the presence of a uniform electric field. When E = (3i + 5j) * 10^5 N/C, the ball is in equilibrium at $$\theta$$ = 37 degrees. Find the charge on the ball and the tension on the string.

====================
|\
|$$\theta$$\
| \
| \ / <- uniform electric field, E = (3i + 5j) * 10^5 N/C
| \/
| O <- charged cork ball, mass = 1g, q = ?


i
^
|
|
-------> j

Homework Equations

F(electric) = qE
F(grav) = mg(-j)

The Attempt at a Solution

I tried using the cosine law with the forces to isolate for $$\theta$$
a^2 = b^2 + c^2 -2bc * cos($$\alpha$$)
but it canceled out.
Anyways,
$$\alpha$$ = $$\theta$$
a = F(elec)
b = F(grav)
c = F(res) = F(elec) + F(grav)

Any ideas? Thanks!

 

[rl.bhat]

In the equilibrium position, resolve mg into two components.
mg*cosθ will provide the tension and mg*sinθ will try to bring the string into vertical position.

The magnitude of the electric field is sqrt(34) and makes an angle α = arctan(5/3)
The electric force on the cork ball is q*E.
In the equilibrium position angle between the string and the electric force is (90 +α - θ )
Its component along the string is Fe*cos(90 +α - θ) and perpendicular to the string is Fe*sin(90 +α - θ ).
Equate them with the components of mg and solve for T and q.