Calculating Charge and Tension in a Uniform Electric Field

[frozen7]

A charges cork ball of mass 1.00g is suspended on a light string in the presence of a uniform electric field has an x compenent of 3.00 x 10^5 N/C and a y component of 5.00 x 10^5 N/C, the ball is in equilibrium at $$\theta$$ = 37 degree. Find:
(a) the charge on the ball
(b) thetension in he string

I do it in this way:

Since the ball is in equilibrum, so the net force acting on the ball is equal to zero. These are 2 forces act on the ball, one is mgcos53 (acting 37 degree below -x-axis), the other one is acting in a opposite direction. Since the ball is in equilibrium, the force which act in opposite direction is equal to mgcos53 as well.
So, we can conclude that the tension in the string is F=mgcos53 and the charge on the ball can be calculated by using the formula : F=qE

Am i doing correctly?

Thanks in advance.

 

[Doc Al]

There are three forces acting on the ball: the weight (which acts downward), the force due to the tension in the string, and the force due to the electric field.

Since the ball is in equilibrium, these forces must add to zero. Consider x and y components separately.

 

[frozen7]

Thanks. Problem solved.