A Van de Graaff generator is a device for generating a large electric potential by building up charge on a hollow metal sphere. A typical classroom-demonstration model has a diameter of 30 cm. How much charge is needed on the sphere for its potential to be 530,000 V?

since we know that electric potential V is equal to kq/r, we can isolate for q, where q= Vr/k, hence q = (530,000)(.15) / (9E9)

Well, let's see, we have a 30 cm diameter sphere and we need to calculate the charge needed for a potential of 530,000 volts. That's quite a shocking question!

Now, when it comes to Van de Graaff generators, the charge they can hold is directly proportional to the potential difference. So, the amount of charge needed can be calculated using the formula:

Charge (Q) = Capacitance (C) × Voltage (V)

Since the capacitance of the hollow metal sphere remains constant, we can calculate it using the formula:

Capacitance (C) = 4πε₀r

where r is the radius of the sphere. In this case, the radius is half of the diameter, so r = 15 cm = 0.15 m.

The value of ε₀, which represents the permittivity of free space, is approximately 8.85 × 10⁻¹² C²/Nm².

Brace yourself for the math!

Calculating the capacitance:

C = 4π(8.85 × 10⁻¹²)(0.15)

Now that we have the capacitance, we can calculate the charge:

Q = C × V

Plugging in the values:

Q = (4π(8.85 × 10⁻¹²)(0.15))(530,000)

Okay, let me do the calculation. *computing*

*Clown Bot's floppy clown shoes tap the floor as it calculates...*

*Ding!*

After solving the equation, we find that the charge needed on the sphere is approximately 0.476 coulombs. That's quite a shocking amount of charge for a little sphere!

Remember, when dealing with electricity, always be careful and keep a safe distance from any large charges. Safety first!

To calculate the charge needed on the sphere of a Van de Graaff generator, we can use the formula:

Q = CV

Where:
Q = charge
C = capacitance
V = potential

The capacitance of a spherical capacitor can be calculated using the formula:

C = 4πε₀r

Where:
C = capacitance
ε₀ = permittivity of free space (8.854 x 10^-12 F/m)
r = radius of the sphere

Given that the diameter of the sphere is 30 cm, the radius will be 15 cm (0.15 m). Plugging this value into the formula, we can calculate the capacitance:

C = 4π(8.854 x 10^-12 F/m)(0.15 m) = 2.107 x 10^-10 F

Now we have the capacitance, we can calculate the charge using the potential:

Q = (2.107 x 10^-10 F)(530,000 V) ≈ 111.9 x 10^-5 C

Therefore, approximately 111.9 microcoulombs (μC) of charge is needed for the sphere to have a potential of 530,000 volts.

To find out how much charge is needed on the sphere of the Van de Graaff generator, we can use the formula for electric potential:

Electric potential (V) = Charge (Q) / Radius (r)

In this case, we know the potential (V = 530,000 V) and the radius (r = 0.15 m or 15 cm).

1. Convert the radius from centimeters to meters:
radius (m) = 0.15 m

2. Rearrange the formula to solve for charge (Q):
Charge (Q) = Electric potential (V) * Radius (r)

3. Substitute the given values into the formula:
Charge (Q) = 530,000 V * 0.15 m

4. Calculate the charge:
Charge (Q) = 79,500 Coulombs

Therefore, to generate a potential of 530,000 V, approximately 79,500 Coulombs of charge is needed on the sphere of the Van de Graaff generator.