# Force between to charged plates

1. Nov 10, 2008

### craka

1. The problem statement, all variables and given/known data
Two thin flat plates measure 1m by 1m and are separated by 0.005m. They are oppositely charged with one plate being +15*10^-6 C and the other -15*10^-6 C.
Estimate the total forces exerted by one plate on the other

2. Relevant equations

F=kq1q2/r^2
$$\int {\vec E \bullet d\vec A} = \frac{{Q_{enc} }}{{\varepsilon _0 }}$$

$$F = qE$$

3. The attempt at a solution

I realised that I attempted this as point charges by the distance between is relatively small in comparison with area
When I did this i calculated it to be 80926 N which is wrong, answer is given as 13N

Than I approached from Guass's law

$$\begin{array}{l} \int {\vec E \bullet d\vec A} = \frac{{Q_{enc} }}{{\varepsilon _0 }} \\ EA = \frac{{Q_{enc} }}{{\varepsilon _0 }} \\ A = 1m^2 \\ E = \frac{{Q_{enc} }}{{\varepsilon _0 A}} \\ \end{array}$$

so electric field from one plate is equal to
$$E = \frac{{15 \times 10^{ - 6} }}{{(8.85 \times 10^{ - 12} ) \times 1}} = 1.695 \times 10^6 N/C$$

and so the force from one plate is
$$\begin{array}{l} F = qE \\ F = (15 \times 10^{ - 6} )(1.695 \times 10^6 )=25.43N \\ \end{array}$$

Anyone able to help me here with this. Thanks

Last edited: Nov 10, 2008