Question

part a
how much energy is stored by the electric field between two square plates, 9.3 cm on a side, separated by a 1.9 - mm air gap? the charges on the plates are equal and opposite and of magnitude 18 nc
express your answer using two significant figures and include the appropriate units.
pe = value units
submit request answer
return to assignment provide feedback

Explanation:

Step1: Calculate the area of the plates

The side - length of the square plate $s = 9.3\ cm=0.093\ m$. The area of a square plate $A=s^{2}=(0.093)^{2}\ m^{2}=8.649\times 10^{-3}\ m^{2}$.

Step2: Calculate the capacitance of the parallel - plate capacitor

The capacitance of a parallel - plate capacitor is given by $C = \frac{\epsilon_{0}A}{d}$, where $\epsilon_{0}=8.85\times 10^{-12}\ F/m$ is the permittivity of free space, $A$ is the area of the plates, and $d = 1.9\ mm = 1.9\times 10^{-3}\ m$ is the separation between the plates.
$C=\frac{8.85\times 10^{-12}\times8.649\times 10^{-3}}{1.9\times 10^{-3}}\ F=4.03\times 10^{-11}\ F$.

Step3: Calculate the energy stored in the capacitor

The energy stored in a capacitor is given by $U=\frac{Q^{2}}{2C}$, where $Q = 18\ nC=18\times 10^{-9}\ C$.
$U=\frac{(18\times 10^{-9})^{2}}{2\times4.03\times 10^{-11}}\ J=\frac{3.24\times 10^{-16}}{8.06\times 10^{-11}}\ J = 4.0\times 10^{-6}\ J$.

Answer:

$4.0\times 10^{-6}\ J$