Show that the capacitance of an insulated spherical conductor is di...

Question

Show that the capacitance of an insulated spherical conductor is directly proportional to the radius of the spherical conductor.

Accepted Answer

📌 Derivation:

Consider an isolated spherical conductor of radius R with charge Q.

Step 1 — Potential on the Surface:
V = kQ/R = Q / (4πε₀R)

Step 2 — Capacitance:
C = Q / V = Q / [Q/(4πε₀R)]

C = 4πε₀R

Step 3 — Proportionality:
Since 4πε₀ is a constant:

┌─────────────────┐
│ C = 4πε₀R │
│ C ∝ R │
└─────────────────┘

∴ Capacitance of a spherical conductor is directly proportional to its radius R.

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