A uniformly charged conducting sphere of 2.4 m diameter has a surface charge density of `80xx10^(-6)cm^(-2)`
a. Find the charge on the sphere.
b. What is the total electric flux leaving the surface of the sphere?

Explanation

(a) Diameter of the sphere ,d =2.4m
Radius of the sphere , r= 1.2m Surface charge density,
`sigma=80.0muC//m^(2)=80xx10^(-6)C//m^(2)`
Total charge on the surface of the sphere.
Q= Charge density `xx` Surface area
`=sigmaxx4pir^(2)`
`=80xx10^(-6)xx4xx3.14xx(1.2)^(2)`
`=1.447xx10^(-3)C`
Therefore , the charge on the surface is `1.447xx10^(-3)C`.
(b) Total electric flux `(phi_("total"))` leaving out the surface of a sphere containing net charge Q is given by the relation ,
`phi_("Total")=(Q)/(epsilon_(0))`
where ,
`epsilon_(0)=` Permittivity of free space
`=8.854xx10^(-12)N^(-1)C^(2)m^(-2)`
`Q=1.447xx10^(-3)C`
`phi_("Total")=(1.44xx10^(-3))/(8.854xx10^(-12))`
`=1.63xx10^(8)NC^(-1)m^(2)`
Therefore , the total electric flux leaving the surface of the sphere is `1.63xx10^(8)NC^(-1)m^(2)`.