Final answer:
To find the required area of the plates of a capacitor with a charge of 4.9 μC and a desired electric field of 2.4 kV/mm, use the equation E = Q / (ε_0 * A) to get A = 0.2307 m^2.
Step-by-step explanation:
To find the area of the plates of a capacitor with a given charge and desired electric field, we can use the relationship between electric field (E), charge (Q), and area (A), as described by the equation
E = Q / (ε_0 * A),
where ε_0 is the permittivity of free space (ε_0 = 8.85 × 10^-12 C^2/N·m^2). With a charge of 4.9 μC (or 4.9 × 10^-6 C) and a desired electric field of 2.4 kV/mm (or 2.4 × 10^6 V/m), we can rearrange the equation to solve for A:
A = Q / (ε_0 * E)
Substituting the values into the equation:
A = (4.9 × 10^-6 C) / (8.85 × 10^-12 C^2/N·m^2 * 2.4 × 10^6 V/m)
A = (4.9 × 10^-6) / (2.124 × 10^-5) m^2
A = 0.2307 m^2
Therefore, the required area for each plate to achieve the desired electric field is 0.2307 m^2.