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What is the capacitance of the earth, assuming it to be a spherical conductor?

User Ali Kanat
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Final answer:

The Earth, when considered as a spherical capacitor, has a capacitance of approximately 709 μF, a total charge of about 2.48 x 105 C, and stores an energy of roughly 3.06 x 1010 J.

Step-by-step explanation:

To calculate the capacitance of the Earth, considered as a spherical capacitor, we need to apply the formula C = 4πε0R, where ε0 is the permittivity of free space and R is the radius of the Earth. The value of ε0 is roughly 8.85 x 10-12 F/m, and the Earth's radius (R) is approximately 6.40 x 106 m. The capacitance C of the Earth then is about 709 μF.

To find the total charge (Q) on this capacitor, we use the relationship Q = CV. Given the potential difference (V) of about 350,000 V, the charge Q is approximately 2.48 x 105 C.

The energy stored in this capacitor can be calculated using the formula E = 0.5CV2, which gives us an energy of about 3.06 x 1010 J.

User Jimmy M
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