Question

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?

Answer 1

(a) Diameter of the sphere, d = 2.4 m

Radius of the sphere, r = 1.2 m
Surface charge density, = 80.0 μC/m² = 80 × 10⁻⁶ C/m²
Total charge on the surface of the sphere,
Q = Charge density × Surface area

Therefore, the charge on the sphere is 1.447 × 10⁻³ C.

(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/ε_o

Where,
ε_o= Permittivity of free space
= 8.854 × 10⁻¹² N⁻¹C² m⁻²
Q = 1.447 × 10⁻³ C 

∴ϕ_Total=(1.447×10⁻³) /(8.854×10⁻¹²)
= 1.63 × 10⁸ N C⁻¹ m²

Therefore, the total electric flux leaving the surface of the sphere is 1.63 × 108 N C⁻¹ m^2.