Question 25.45: A certain parallel-plate capacitor is filled with a dielectr......
A certain parallel-plate capacitor is filled with a dielectric for which \kappa = 5.5.The area of each plate is 0.034 m², and the plates are separated by 2.0 mm. The capacitor will fail (short out and burn up) if the electric field between the plates exceeds 200 kN/C. What is the maximum energy that can be stored in the capacitor?
Using Eq. 25-29, with σ = q/A, we have
E=\frac{\sigma}{\kappa \varepsilon_0} (25-29)
|\vec{E}|=\frac{q}{\kappa \varepsilon_0 A}=200 \times 10^3 \,N / C
which yields q=3.3 \times 10^{-7}\, C . Eq. 25-21 and Eq. 25-27 therefore lead to
C=\kappa \varepsilon_0 \mathscr{L} =\kappa C_{\text {air }} (25-27)
U=\frac{q^2}{2 C} (potential energy). (25-21)
U=\frac{q^2}{2 C}=\frac{q^2 d}{2 \kappa \varepsilon_0 A}=6.6 \times 10^{-5}\, J .