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Step By Step Answers with Explanation

Derivation of the Capacitance of a Single Spherical Shell:

Step 1: Gather Information

Where:

- \(C\) is the capacitance in Farads (F).

Step 4: Electric Field Outside the Spherical Shell

Outside the shell, the electric field behaves as if all the charge is concentrated at the center of the sphere.

\[ V = \frac{kQ}{r} \]

Where:

Now we have the expression for the capacitance of a single spherical shell:

\[ C = \frac{R}{k} \]

We already have the expression for capacitance:

\[ C = \frac{R}{k} \]

- Radius of the Earth, \(R_{\text{Earth}} = 6,371,000 \, \text{m}\) (approximately).

- Coulomb's constant, \(k = 8.99 \times 10^9 \, \text{N}\cdot\text{m}^2/\text{C}^2\).