Question

400 micro coulomb charge is uniformly spread over the surface of a spherical shell and surface density is 0.314 C/m-2. What is the radius of this shell?

Answer 1

Given:

400 micro coulomb charge is uniformly spread over the surface of a spherical shell and surface density is 0.314 C/m-2.

To find:

What is the radius of this shell?

Solution:

From given, we have,

400 micro coulomb charge is uniformly spread over the surface of a spherical shell and surface density is 0.314 C/m-2.

⇒ Charge = 400 × 10^{-6} C

⇒ Surface charge density = 0.314 C/m-2.

Surface area of spherical shell = 4πr²

We use the formula,

Surface charge density = Charge / Surface area

0.314 = 400 × 10^{-6} / 4πr²

0.314 = 400 × 10^{-6} / (4 × 3.14 × r²)

⇒ r² = (400 × 10^{-6} ) / (0.314 × 4 × 3.14)

⇒ r² = 1 × 10^{-4}

∴ r = 0.001 m.