A uniformly charged conducting sphere of 2.4 m diameter has a surface charge density of 80.0 μC/m². (a) Find the charge on the sphere. (b) What is the total electric flux leaving the surface of the sphere?

Solution

Given, D iameter of the sphere = 2.4 ∴ R adius of sphere, r = \frac{2.4}{2} = 1.2 m S urface charghe density of conducting sphere, σ = 80 \times 10^{- 6} C / m^{2}

(a) Charge on sphere

σ . A = σ . 4 {πr}^{2}

q = 80 \times 10^{- 6} \times 4 \times 3.14 \times (1.2)^{2} q = 1.45 \times 10^{- 3} C

(b) The total electric flux leaving the surface of the sphere
using the gauss formula,

ϕ = \frac{q}{ε_{0}} = \frac{1.45 \times 10^{- 3}}{8.854 \times 10^{- 12}} = 1.6 \times 10^{8} {Nm}^{2} / C

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