Question

Surface density of charge on a charged conducting sphere of radius R in terms of electric field intensity E at a distance r in free space is ____________.

(r > R, ε₀ = permittivity of free space)

Options

• `ε_0 "E"("R"/"r")^2`

• `ε_0 "E""R"/"r"`

• `ε_0 "E"("r"/"R")^2`

• `ε_0 "E""r"/"R"`

Answer 1

Surface density of charge on a charged conducting sphere of radius R in terms of electric field intensity E at a distance r in free space is `underline(ε_0 "E"("r"/"R")^2)`.

Explanation:

The electric field intensity at a distance r from the conducting sphere is

E = `1/(4πε_0) "Q"/"r"^2` ..............(i)

The surface charge density of sphere is

σ = `"Q"/(4π"R"^2)` ....................(ii)

Dividing Eqs. (ii) by (i), we get

`σ/"E" = "Q"/(4π"R"^2) xx (4πε_0"r"^2)/"Q" = ε_0("r"/"R")^2`

or σ = `ε_0 "E"("r"/"R")^2`