Total Charge on a Sphere

 

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:

Q = ∫₀ᴿ ρ(r) 4πr² dr