Capacitance of a Spherical Shell?

📌 CONCEPT: The capacitance of a spherical shell is the ratio of the charge on the shell to the potential difference between the shell and the surrounding space, and it is a measure of its ability to store electric charge.

📐 RULE / FORMULA: The capacitance (C) of a spherical shell is given by the formula C = 4πε₀R, where ε₀ is the electric constant (also known as the permittivity of free space) and R is the radius of the shell.

💡 WORKED EXAMPLE: Suppose we have a spherical shell of radius 10 cm with a charge of 1 μC distributed uniformly over its surface. Using the formula C = 4πε₀R, we can calculate its capacitance. First, we need to find the value of ε₀, which is approximately 8.854 × 10^(-12) F/m. Then, we can plug in the values to get C = (4 × 3.14 × 8.854 × 10^(-12)) / (0.1) ≈ 3.44 × 10^(-10) F. Therefore, the capacitance of the spherical shell is approximately 3.44 × 10^(-10) F.

⚠️ COMMON MISTAKE: Students often forget to consider the surrounding space and assume the shell's capacitance is the same as a point charge, which can lead to incorrect calculations.