EMC Question of the Week: March 23, 2026

A metal sphere the size of a basketball (diameter = 24 cm) has an absolute capacitance of 13 pF. A metal sphere the size of a tennis ball (diameter = 6.7 cm) has an absolute capacitance of 3.7 pF. If they were separated by a distance of 10 cm, the measured capacitance between them would be about   

1. 17 pF
2. 13 pF
3. 9.3 pF
4. 3.7 pF

Answer

The best answer is “d.” The exact value of the capacitance between two objects would be the series combination of their self-capacitances, in parallel with their mutual capacitance. However, when one object is much larger than the other, its self-capacitance is approximately equal to its absolute capacitance. So, C₁ in the figure is approximately 13 pF. Also, when the smaller object is separated from the larger object by more than its own diameter, its capacitance to the larger object is approximately equal to its absolute capacitance. So the measured capacitance between the two spheres is approximately the absolute capacitance of the smaller sphere.

That's why objects we measure on earth have a measured capacitance (to the earth) equal to their own absolute capacitance. This is true at almost any distance from the earth unless the object is close to the earth relative to its own diameter. It's also why floating metal objects in a system typically have a capacitance to system ground that approximately equals the absolute capacitance of the object.

Note: Of the four possible answers provided, 3.7 pF is the best estimate. However, the rough nature of this calculation doesn't warrant two significant figures. 

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