Finding Total Charge on a Sphere
Basic Formula
Q = ∫ ρ dV
Given
- Radius R = 30 cm = 0.3 m
- Charge density ρ = 200 pC/m³ = 200 × 10-12 C/m³
Step 1: Volume of Sphere
V = (4/3) π R³
V = (4/3) π (0.3)³
V = (4/3) π (0.027)
V ≈ 0.113 m³
Step 2: Total Charge
Q = ρ × V
Q = (200 × 10-12) × 0.113
Q ≈ 22.6 × 10-12 C
Final Answer
Q ≈ 2.26 × 10-11 C
Important Note:
The solution assumes charge density is constant.
If density varies with radius, then:
The solution assumes charge density is constant.
If density varies with radius, then:
Q = ∫₀ᴿ ρ(r) 4πr² dr