If a capacitor has opposite 5.3 micro-Coloumb charges on the plates, and an electric field of 2.3 kV/mm is desired between the plates, what must each plate's area be?
To calculate the required plate area, you can use the formula for the electric field between parallel plates:
Electric field (E) = Voltage (V) / Distance (d)
The given electric field is 2.3 kV/mm, which can be converted to V/m by dividing by 1000 since 1 kV = 1000 V and multiplying by 1000 since 1 mm = 1/1000 m.
Therefore, Electric field (E) = 2.3 kV/mm × (1000 V/kV) × (1000 mm/m) = 2.3 × 10^6 V/m
Now, rearrange the formula to solve for voltage:
Voltage (V) = Electric field (E) × Distance (d)
Since the distance between the plates is not given, we cannot directly calculate the voltage from this equation. However, we can use the equation Q = C × V, where Q is the charge on the plates and C is the capacitance of the capacitor.
The charge on the plates is given as 5.3 micro-Coloumbs, which can be converted to Coloumbs by dividing by 1,000,000.
Therefore, Charge (Q) = 5.3 × 10^(-6) Coloumbs
The capacitance (C) of a capacitor is given by the formula:
Capacitance (C) = Charge (Q) / Voltage (V)
Now rearrange this formula to solve for voltage:
Voltage (V) = Charge (Q) / Capacitance (C)
Using the given charge of 5.3 × 10^(-6) Coloumbs and rearranging the formula, we can find the voltage. However, the capacitance is not given, so we cannot directly calculate the voltage.
Without the value of capacitance, it is not possible to determine the required plate area using the information provided. You would need the capacitance value, or additional information to calculate the required plate area for the desired electric field.