Each Plate of an Ideal Air-Filled Parallel-Plate Capacitor Has an Area

Multiple Choice

Each plate of an ideal air-filled parallel-plate capacitor has an area of $0.0020 \mathrm {~m} ^ { 2 }$ , and the separation of the plates is $0.090 \mathrm {~mm}$ . An electric field of $2.1 \times 10 ^ { 6 } \mathrm {~N} / \mathrm { C }$ is present between the plates. What is the surface charge density on the plates? $\left( \varepsilon _ { 0 } = 8.85 \times 10 ^ { - 12 } \mathrm { C } ^ { 2 } / \mathrm { N } \cdot \mathrm { m } ^ { 2 } \right)$

A) $28 \mu \mathrm { C } / \mathrm { m } ^ { 2 }$
B) $47 \mu \mathrm { C } / \mathrm { m } ^ { 2 }$
C) $9.3 \mu \mathrm { C } / \mathrm { m } ^ { 2 }$
D) $39 \mu \mathrm { C } / \mathrm { m } ^ { 2 }$
E) $19 \mu \mathrm { C } / \mathrm { m } ^ { 2 }$