The dome of a Van de Graaff generator has a diameter of 32.0 cm and is surrounded by dry air with a 'breakdown' electric field of 3.00 106 V/m.
What is the maximum potential of the dome?
To find the maximum potential of the dome of a Van de Graaff generator, we need to calculate the maximum voltage that can be applied to it without causing a breakdown of the surrounding air.
The electric field required for a breakdown to occur is given as 3.00 * 10^6 V/m. The electric field can be calculated using the formula:
Electric Field (E) = Voltage (V) / Distance (d)
We know the diameter of the dome is 32.0 cm, which means the radius (r) is half of that, or 16.0 cm. This can be converted to meters by dividing by 100, so the radius is 0.16 meters.
Since the dome of the Van de Graaff generator is a sphere, the distance from the center of the dome to any point on its surface is equal to the radius (r). Therefore, the distance (d) in this case is also 0.16 meters.
Now, we can rearrange the formula to solve for the voltage (V):
V = E * d
Plugging in the values:
V = (3.00 * 10^6 V/m) * (0.16 m)
V ≈ 4.80 * 10^5 volts
Therefore, the maximum potential of the dome of the Van de Graaff generator is approximately 4.80 * 10^5 volts.