Force between to charged plates

[craka]

Homework Statement

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

Homework Equations

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

$$F = qE$$

The Attempt at a Solution

I realized 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

 

[Jhero]

Thank you for your question. Based on the information given, it seems that the total forces exerted by one plate on the other should be the sum of the attractive and repulsive forces between them. Using the equation F=kq1q2/r^2, we can calculate the attractive force between the plates:

F_attractive = (8.99x10^9 Nm^2/C^2)(15x10^-6 C)(15x10^-6 C)/(0.005m)^2 = 13.5 N

And using the same equation, we can calculate the repulsive force between the plates:

F_repulsive = (8.99x10^9 Nm^2/C^2)(15x10^-6 C)(-15x10^-6 C)/(0.005m)^2 = -13.5 N

Therefore, the total force exerted by one plate on the other is the sum of these two forces, which is 13.5 + (-13.5) = 0 N. This means that the plates will not experience any net force on each other, as they are equally charged and the attractive and repulsive forces cancel each other out.

I hope this helps clarify the situation. If you have any further questions, please don't hesitate to ask.