Capacitance of a Sphere: A Quick Calculation Method

[arydberg]

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

 

[kuruman]

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.

 

[tech99]

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.

 

[vanhees71]

Note that this refers to the non-rationalized (Gaussian) cgs system of units!

 

[arydberg]

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

 

[nasu]

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.

 

[rude man]

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.