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?

• Ans (a).

Since diameter of the sphere, d = 4 m,

therefore Radius of the sphere, r = 1.2 m

Surface charge density, σ =80.0 µC/m² = 80 x 10^-6 C/m²

Total charge on the surface of the sphere,

Q = Charge density x Surface area = σ x 4 π r² = 80 x 10^-6 x 4 x 3.14 x (1.2)² = 1.447 x 10^-3 C Therefore, the charge on the sphere is 1.447 x 10^-3 C.

Ans (b).

Total electric flux (Φ_Total ) leaving out the surface of a sphere containing net charge Q is given by the relation,

Φ_Total =Q/ε₀ 

Where, ε₀ = Permittivity of free space = 8.854 x 10^-12 N^-1C² m^-2

Q = 1.447 x 10^–3C

Therefore Φ_Total =Q/ε_{0 = ( 1.447 x 10^–3})/(8.854 x 10^-12 )

= 1.63 x 10⁸NC^-1m²

Therefore, the total electric flux leaving the surface of the sphere is 1.63 x 10⁸ N C^-1 m².