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?
Solution
(a) Diameter of the sphere, d = 2.4 m
Radius of the sphere, r = 1.2 m
Surface charge density, `sigma` = 80.0 μC/m2 = 80 × 10−6 C/m2
Total charge on the surface of the sphere,
Q = Charge density × Surface area
= `sigma xx 4pir^2`
= 80 × 10−6 × 4 × 3.14 × (1.2)2
= 1.447 × 10−3 C
Therefore, the charge on the sphere is 1.447 × 10−3 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,
∈0 = Permittivity of free space
= 8.854 × 10−12 N−1 C2 m−2
Q = 1.447 × 10−3 C
`phi_"total" = (1.44 xx 10^-3)/(8.854 xx 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 m2.
