Radius of object in electric field

[user977784078]

Homework Statement

Two parallel plates with opposite charges are 0.01 m apart and have a potential difference of 100 V. A charged spherical object has 20 excess electrons stays motionless between the plates. If the density of the object is 1000 kg/m^3, what is the radius of the spherical object?

Homework Equations

E=V/d
Fq=qE
Fg=mg
density=m/Vs
Vs = 4/3 pi r^3

The Attempt at a Solution

I equated the electric force and the gravitational force as they are equal.

E = 100/0.01=10000 vollts/m

Therefore, Fq = 20 x 1.602x10^-19 x 10000 = 3.204x10^-14

Fg=m x 9.81 (I am assuming that I don't need to use the universal law of gravity because I don't know how high the apparatus is off the ground).

Therefore, Fg=Fq => m x 9.81 = 3.204x10^-14 => m = 3.27 x 10^-15 kg

density = m/Vs => Vs = m/density = 3.27 x 10^-18

Vs = 4/3 pi r^3 => r = 0.92x10^-6 meters or 0.92 micro meters.

However, this answer is wrong.

Where have I gone wrong?

Thank you for helping.

 

[ehild]

I do not see anything wrong in your derivation and result.

ehild

 

[user977784078]

I thought so. Must be a mistake with the automated quiz.

 

[nasu]

Have you tried 0.9 instead of 0.92? All your given values have only 1 significant digit.