charge on a ball

[1517279]

1. The problem statement, all variables and given/known data
An electric field E=141000.0i N/C causes the 4.70 g ball in the picture to hang at a α=22.9° angle. What is the charge on the ball?


2. Relevant equations
E=(1/4pieE)*(q/r^2)

3. The attempt at a solution
I tried solving this question first by drawing a force diagram on the charged particle. On the diagram:
W = T cos α -1
F = T sin α -2

I divided equation 2 by 1
I get tan α = F/mg ; since F = 1/4pie * q/r^2; i subbed it in
therefore: mgtanα4pie*r^2 = q

but i am having trouble in solving for r; i tried solving for r by using the Pythagorus theorem, but i didnt workout... i'm kinda stuck, i guess its because the known value for E field is in a component form...

can someone please guide me through this question



picture is attatched
thanks in advance.

[LowlyPion]

What picture?
How long is the string?

[1517279]

length of the string is not given

[Doc Al]

2. Relevant equations
E=(1/4pieE)*(q/r^2)
That's the field of a point charge--not relevant here. You are given the field.

3. The attempt at a solution
I tried solving this question first by drawing a force diagram on the charged particle. On the diagram:
W = T cos α -1
F = T sin α -2

I divided equation 2 by 1
I get tan α = F/mg ;
This is fine.
since F = 1/4pie * q/r^2;
This is not. What force does a field E exert on a charge q?

[1517279]

k it should be f=1/4pieEo *q/r^2 then right?

[Doc Al]

k it should be f=1/4pieEo *q/r^2 then right?
No. Again, that's the field surrounding a point charge--not relevant here. You have a uniform field given; you need to find the force that given field exerts on the charge. (What's the definition of electric field?)