Question

Question 1.22: A uniformly charged conducting sphere of 2.4 m diameter has a surface charge density of 80.0 μC/m 2 . (a) Find the charge on the sphere. (b) What is the total electric flux leaving the surface of the sphere?

Class 12 - Physics - Electric Charges And Fields Electric Charges And Fields Page-48

Answer 1

(a) diameter of uniformly charged conducting sphere, d = 2.4 m
so, radius , R= d/2 = 2.4/2 = 1.2 m
surface charge density of charged conducting sphere , σ = 80 microC/m²

as we know, surface charge density = charge on sphere /surface area of sphere,
e.g., $\bf{\sigma=\frac{q}{4\pi r^2}}$
now, q = 4πr²σ
q = 4 × 3.14 × (1.2)² × 80 × 10^-6 [ 1 microC = 10^-6 C]
q = 12.56 × 1.44 × 80 × 10^-6 C
q = 1.45 × 10^-3 C
hence, charge on sphere, q = 1.45 × 10^-3C

(b) according to Gauss law, $\bf{\phi=\frac{q}{\epsilon_0}}$
= 1.45 × 10^-3/8.85 × 10^-12
= 1.64 × 10^8 Nm²/C
hence, electric flux leaving the surface of the sphere is 1.64 × 10^8 Nm²/C