Electric Field of ping pong ball of mass

[llamajuice]

Homework Statement

A ping pong ball of mass 3.0 x 10^-4 kg hangs from a light thread 1.0m long, between 2 vertical parallel plates 10.0cm apart. When the potential difference across the plates is 420 V, the ball comes to equilibrium 1.0 cm to one side of its original position.
a) Calculate the electric field strength between the plates.
b) Calculate the tension in the thread
c) Calculate the magnitude of the electric force deflecting the ball..
d) Calculate the charge on the ball.

Homework Equations

Epsilon = (kq)/r^2
Electrical Force = (kq1q2)/r^2
V = (kq)/r

The Attempt at a Solution

a)Epsilon = V/r = 420V/0.10m = 4200N/C

b) Fg = mg = (3.0 x 10^-4 kg)(9.8m/s^2) = 2.94 x 10^-3N

c)I'm not sure how to do the rest.

 

[llamajuice]

Here's what the diagram looks like.

 

[graphene]

b) is wrong.
Draw a free body diagram with the ball 1cm away from one of the plates, show all the forces acting on the ball.

 

[llamajuice]

Something like this?

 

[Jindo]

b) alpha is angel between the thread (when V = 420V) and vertical
alpha~sin(alpha)=0.01/1 =0.01 (rad)
the tension in the thread (T):
Because of equilibrium condition:
Fg/T = cos(alpha) --> T = Fg/cos(alpha)
c) the magnitude of the electric force deflecting the ball
Fe/Fg =tan(alpha)~alpha --> Fe = Fg.0.1
d) Fe=q.E --> q= Fe/E = Fe.r/V

 

[graphene]

the FBD looks alright.

Notate the angle between the string & the vertical.

Then balance the forces acting on the ball.
That should solve b,c & d. :)