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?

Given: radius of sphere, r = 1.2 m


Surface charge density, σ = 80.0 μC/m2



a) Let charge on sphere = q


We understand that,


Total charge, Q = Surface charge density × surface area.


Surface area of sphere, S = 4πr2


S = 18.08 m2


Q = 80 × 10-6Cm-2 × 18.08m-2


Q = 1.447 × 10-3C


b) Let total electric flux leaving the surface of sphere =


We know that,


Flux, Φ = q/ε0 …(1)


Where, Q = net charged.


ε0 = permittivity of free space


ε0 = 8.85 × 10-12N-1 m-2C2


By, plugging the values of q and ε0 in equation (1), we get,



Φ = 1.63 × 108 Nm2C-1


The total flux through the sphere is 1.63 × 108 Nm2C-1 .


28