A charged ball on a string between two charged plates

[Karol]

Homework Statement

A charged ball of mass 0.2[gr] and q=6E-9[Coulomb] hangs on a string between 2 plates that are 5[cm] apart. the ball makes 30⁰ with the vertical. what is the voltage difference of the plates.

Homework Equations

Electric field: $$E[\frac{N}{Coulomb}]=\frac{V}{S[m]}$$
The force: $$F=E\cdot q$$

The Attempt at a Solution

The horizontal force: $$F_x=mg\cdot \tan 30^0=2E-4[Kg]\cdot 10\cdot \tan 30^0=11E-6[N]$$
The field: $$11E-6[N]=E\cdot 6E-9[Coulomb]\rightarrow E=1924.5[V]$$
Seems small.
$E=\frac{V}{0.05[m]}\rightarrow 1924.5=\frac{V}{0.05[m]} \rightarrow V=96[V]$
It should be 9440[V]

 

[ehild]

Homework Statement

A charged ball of mass 0.2[gr] and q=6E-9[Coulomb] hangs on a string between 2 plates that are 5[cm] apart. the ball makes 30⁰ with the vertical. what is the voltage difference of the plates.

Homework Equations

Electric field: $$E[\frac{N}{Coulomb}]=\frac{V}{S[m]}$$
The force: $$F=E\cdot q$$

What is the direction of the electric force?

The Attempt at a Solution

The horizontal force: $$F_x=mg\cdot \tan 30^0=2E-4[Kg]\cdot 10\cdot \tan 30^0=11E-6[N]$$

You mean $$F_x=mg\cdot \tan 30^0=2\cdot 10^{-4}\cdot 10\cdot \tan 30^0=11\cdot10^{-6}[N]$$
Use g=9.8 m/s², and do not round off so much. And check the magnitude of the force.

 

[Karol]

Thanks, i solved