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.

 

[HalfLostAndSearching]

Your approach is correct, but your calculation for the electric force is incorrect. The electric force should be calculated using the charge of the object (20 excess electrons) and the electric field (10000 volts/m). So the correct calculation for the electric force would be:

Fq = 20 x 1.602x10^-19 x 10000 = 3.204x10^-15 N

Using this value for the electric force, you would get a correct value for the mass of the object and therefore the correct radius. Your final answer should be:

r = 1.41x10^-6 meters or 1.41 micrometers.