Q 1.22)

A uniformly charged conducting sphere of 2.4 m diameter has a surface charge density of 80.0 μC /m 2

(a) Find the charge on the sphere.

(b) What is the total electric flux leaving the surface of the sphere?


 

At a distance ( d ) from the center of a sphere, the electric field intensity:

E=14πϵ0.qd2

So the net charge on the sphere:

q=E(4πε0)d2=1.5×1039×109=6.67×109C=6.67nC

The net charge on the sphere is 6.67 nC.

 


(a)

The radius of the sphere, r = 1.2 m

Surface charge density, σ = 80.0 μC /m 2 = 80 × 10 – 6 C/m 2

The total charge on the surface of the sphere:

Q = Charge density × Surface area

= σ × 4πr 2

= 80 × 10– 6 × 4 × 3.14 × ( 1.2 )2

= 1.447 × 10– 3 C

The charge on the sphere is 1.447 × 10– 3 C.

(b) Total electric flux ( ϕ Total  ) leaving out the surface:

ϕTotal=qϵ0

 ϕTotal=1.447×1038.854×1012=1.63×108NC1m2

The total electric flux leaving the surface of the sphere is 1.63 × 10 8 N C – 1 m 2