Each Plate of a Parallel-Plate Air-Filled Capacitor Has an Area $0.0040 \mathrm {~m} ^ { 2 }$

Multiple Choice

Each plate of a parallel-plate air-filled capacitor has an area of $0.0040 \mathrm {~m} ^ { 2 }$ , and the separation of the plates is $0.020 \mathrm {~mm}$ . An electric field of $8.2 \times 10 ^ { 6 } \mathrm {~N} / \mathrm { C }$ is present between the plates. What is the energy density in the region between the plates? $\left( \varepsilon _ { 0 } = 8.85 \times 10 ^ { - 12 } \mathrm { C } ^ { 2 } / \mathrm { N } \cdot \mathrm { m } ^ { 2 } \right)$

A) $610 \mathrm {~J} / \mathrm { m } ^ { 3 }$
B) $500 \mathrm {~J} / \mathrm { m } ^ { 3 }$
C) $400 \mathrm {~J} / \mathrm { m } ^ { 3 }$
D) $300 \mathrm {~J} / \mathrm { m } ^ { 3 }$
E) $200 \mathrm {~J} / \mathrm { m } ^ { 3 }$