Amount of charge spherical conductor can hold in air

[jh12]

I'm a little thrown off by this because we there is no voltage value given...
And how does the air play into the problem? I just something to help me get started:

What is the maximum amount of charge that a spherical conductor of radius 5.0 cm can hold in air?

 

[hage567]

http://en.wikipedia.org/wiki/Electrical_breakdown

The "Mechanism" section should answer your question about why the air is important.

 

[astrokreng]

The maximum amount of charge that a spherical conductor can hold is dependent on several factors, including its radius and the surrounding environment. In the case of a spherical conductor in air, the amount of charge it can hold is influenced by the dielectric strength of air, which is the maximum electric field that air can withstand before breaking down and becoming conductive. This value is typically around 3 million volts per meter for air at standard temperature and pressure.

Without knowing the voltage value, it is difficult to determine the exact amount of charge that a spherical conductor of radius 5.0 cm can hold in air. However, we can use the formula Q = CV, where Q is the charge, C is the capacitance (a measure of how much charge a conductor can hold), and V is the voltage. Since we do not have a specific voltage value, we can estimate the maximum charge by assuming a typical voltage value for air. For example, if we assume a voltage of 1000 volts, the maximum charge that a spherical conductor of radius 5.0 cm can hold would be approximately 0.088 microcoulombs.

It is important to note that this estimation is based on ideal conditions, and real-world factors such as surface imperfections and humidity can affect the actual amount of charge a spherical conductor can hold. Additionally, the charge that a spherical conductor can hold may also be limited by the breakdown strength of the material it is made of. Overall, the maximum amount of charge that a spherical conductor can hold in air is a complex and dynamic concept that is influenced by multiple factors.