Final answer:
To achieve an electric field of 510 V/m between two parallel plates 15.0 mm apart, a potential difference of 7.65 V is needed. The calculation uses the formula E = V/d, resulting in V being 7.65 volts for the given electric field strength and distance.
Step-by-step explanation:
Calculating Electric Field and Voltage
To find the electric field (E) between two parallel plates, use the formula E = V/d, where V is the potential difference and d is the distance between the plates. For a desired electric field of 510 V/m and plates separated by 15.0 mm (or 0.015 m), the potential difference V needed is calculated by rearranging the formula to V = E × d. Plugging in the values, we get V = 510 V/m × 0.015 m, which equals 7.65 V.
Therefore, to achieve an electric field of 510 V/m between the two plates that are 15.0 mm apart, a potential difference of 7.65 volts must be applied across the plates.
It's also important to ensure that the electric field does not exceed the breakdown strength for air to avoid electrical discharge through the air.