# 400 pC charge is uniformly spread over the surface of a spherical shell and surface density is 0.314 C-2. What is the radius of this shell ?

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by (630 points)

Suppose § represents surface charge density.

then § = Charge/ surface area

now surface area = 4 ¤ r2 where ¤ = pie

⇒ 0.314 = 400 × 10 -12 C / 4 × 3.14 × r2

on solving and simplfying,  r= 10000 × 10-9 / 314 × 314

⇒ r = 0.0000100709

by (29 points)

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.