Electromagnetism

Question

A spherical ball of plasma has a radius of 2m. The electric field on the surface of the ball is measured to be 4.7x10^4 N/C and points radially inward toward the centre. What is the average volume charge density of the plasma?

Answer 1

Given:

R = 2 m

E_surface = -4.7 (10⁴) N / C

Find:

ρ = ? N / (C * m³)

Solution:

E = k Q / R²

Q = ρ * V = ρ * 4 / 3 π R³

k Q / R² = k * ρ * 4 / 3 π R

E = k * ρ * 4 / 3 * π * R

ρ = 3 * E / ( 4 * k * π * R ) = 3 * ( -4.7 (10⁴) ) / [ 4 * (8.99 (10⁹) * π * 2 ]

∴ ρ ≈ - 6.24 (10^-7) N / (C * m³)

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