Question

A cylinder is charged by 10 mC. Length of the cylinder is 1km and radius is 1mm . Surface density of charge of cylinder is

Answer 1

Given :

• Charge on cylinder q = 10 mC
• Length of cylinder L = 1 km = 1000 m
• Radius of cylinder r = 1 mm = 10⁻³ m

To find :

• Surface charge density

Solution :

• Let the surface charge density be denoted by σ .
• We know that, surface charge density is given by the charge per unit surface area.

    ∴ σ = q ÷ A

• Surface Area of cylinder is given by ,

        A = π r² L

     ∴ A = π × ( 10⁻³ )² × (10³)

     ∴ A = 3.14 × 10⁻³ m²

• σ = (10 × 10⁻³) ÷ ( 3.14 × 10⁻³)

    ∴ σ = 3.18 C/m²

Answer : The surface charge density is 3.18 C/m² .