Electrostatics and electric charge and field

[chiurox]

Homework Statement

A charged sphere is suspended by a nonconductive string in a uniform horizontal electric field. The electric field exerts a force on the sphere such that its equilibrium position is diplaced at an angle  = 30° relative to the vertical, as shown in the diagram below. The mass of the sphere is m = 4.0x10-3 kg, and the charge on the sphere is q = -3 uC.

a. What is the force on the sphere exerted by the electric charge?

b. What are the magnitude and the direction of the electric field?

c. The sphere is released from the string. What are the magnitude and the direction of the sphere's subsequent acceleration?

Homework Equations

F=k[(|q_1|q_2|)/r²]
E=F/q_o

The Attempt at a Solution

a)
I first tried to find the length of the displacement due to the force:
tan(theta)=F_E / F_mg
tan(30)=F_E / (9.8)(0.004)
F_E = 0.02 N is this correct?

b)
E=F/q_o
E=0.02 / -3
E=-0.0067 N/C correct?

c)I think the force would be the vertical component of the Electric Force (up) minus gravity, and the direction of the acceleration would be down (-). But how do I find the vertical component of the electrical force?

Thanks

 

[jandl]

If you do a sum of forces in the x and y directions and set them equal to zero you should have two equations (one for each direction) and two unknowns (the electric field strength and the tension in the string). This will give you the answers to both parts a and b.

Think about what happens when the sphere is released, how could you change the value of the tension in the equations to represent this?