1.

A uniformly charged conducting sphere of 2.4m diameter has a surface density of `80.0 mu C//m^(2)`. (a) Find the charge on the sphere (b) What is the total electric flux leaving the surface of the sphere ?

Answer» (a) Diameter of the sphere, d = 2.4 m ltBrgt Radius of the sphere, r = 1.2 m
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 sphere 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)/(in_(0))`
Where,
`in_(0)` = Permittivity of free space ltBrgt `=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)`.


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