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Question 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

(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

0  = 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−1 m2.

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