Question
1.22: 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?
Answer:
Method - 1
(a) Diameter of the sphere, d = 2.4 m
Radius of the sphere, r = 1.2 m
Surface charge
density, = 80.0 µC/m2 = 80 × 10−6 C/m2
Total charge
on the surface of the sphere,
Q = Charge density × Surface area
= 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 ( ) leaving out the
surface of a sphere containing net charge Q is given by the relation,
Where,
∴0 = Permittivity of free
space
8.854 × 10−12 N−1C2 m−2 Q = 1.447 × 10−3 C
1.63 × 108 N C−1 m2
Therefore, the total
electric flux leaving the surface of the sphere is 1.63 × 108 N C−1m2.
Method - 2 
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