Capacitance of a Sphere: A Quick Calculation Method

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    Capacitance Sphere
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Discussion Overview

The discussion revolves around the calculation of the capacitance of a one-foot diameter metal sphere. Participants explore different methods and units for determining capacitance, including comparisons between the Centimetre-Gram-Second (cgs) system and the International System of Units (SI).

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant asks for the capacitance of a one-foot diameter metal sphere, noting it is a one-terminal component and suggesting a relationship between charge and voltage (C = Q/V).
  • Another participant suggests looking up the capacitance of a concentric spherical capacitor and mentions the need to convert the diameter to SI units for numerical answers.
  • It is noted that in the cgs system, the capacitance of a sphere is equal to its radius in centimetres, with a conversion factor indicating that 1 cm is approximately equal to 1.11 pF.
  • A clarification is provided that this reference to capacitance in the cgs system pertains to the non-rationalized (Gaussian) version.
  • In SI units, the capacitance is stated as ##4\pi \epsilon_0R##, or approximately ##R/(9\times 10^9)##, which aligns with previous mentions of capacitance.
  • A participant reiterates the initial question about the capacitance of the sphere, emphasizing the relationship between voltage, charge, and capacitance.

Areas of Agreement / Disagreement

Participants present multiple methods and units for calculating capacitance, with no consensus reached on a single approach or final answer. Disagreement exists regarding the preferred system of units and the implications of different calculations.

Contextual Notes

Limitations include potential confusion between different unit systems (cgs vs. SI) and the need for conversions. The discussion does not resolve the implications of these differences on the final capacitance value.

arydberg
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Could anyone tell me the capacitance of a one food diameter metal sphere. I know that this is a one terminal component but it still should have a capacitance. If a charge of Q is small and a 6 inch radius is drawn about the point then that 6 inch radius ( 12 in diameter ) should have a voltage associated with it. C = Q/V

Thanks
 
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arydberg said:
Summary:: capacitance of a sphere

Could anyone tell me the capacitance of a one food diameter metal sphere. I know that this is a one terminal component but it still should have a capacitance. If a charge of Q is small and a 6 inch radius is drawn about the point then that 6 inch radius ( 12 in diameter ) should have a voltage associated with it. C = Q/V

Thanks
Look up the capacitance of a concentric spherical capacitor and then make the outer sphere radius infinitely large. To find a numerical answer, don't forget to convert the one food diameter to conventional SI units.
 
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It may be handy to know that in the Centimetre-Gram-Second (cgs) system of units, the capacitance of a sphere is equal to its radius, and the unit of capacitance is the centimetre. By good fortune, a centimetre of capacitance is approximately equal to a picofarad. 1cm = 1.11pF. So the capacitance of a sphere is approximately equal to its radius in centimetres.
 
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Note that this refers to the non-rationalized (Gaussian) cgs system of units!
 
tech99 said:
It may be handy to know that in the Centimetre-Gram-Second (cgs) system of units, the capacitance of a sphere is equal to its radius, and the unit of capacitance is the centimetre. By good fortune, a centimetre of capacitance is approximately equal to a picofarad. 1cm = 1.11pF. So the capacitance of a sphere is approximately equal to its radius in centimetres.
Thank you
 
In SI units the capacitance is ##4\pi \epsilon_0R## or about ##R/(9\times 10^9)##. The result is the same as the one mentioned by tech99.
 
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arydberg said:
Summary:: capacitance of a sphere

Could anyone tell me the capacitance of a one food diameter metal sphere. I know that this is a one terminal component but it still should have a capacitance. If a charge of Q is small and a 6 inch radius is drawn about the point then that 6 inch radius ( 12 in diameter ) should have a voltage associated with it. C = Q/V

Thanks
Right, and it's a quick way to come up with the capacitance of the sphere:
V = kQ/a = Q/C, k = 9e9 SI.
 

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