Auniformly charged conducting sphere of 2.4 m diameter has a surfacecharge density of 80.0 μC/m2.(a) Find the charge on the sphere. (b) What is the total electricflux leaving the surface of the sphere?
Auniformly charged conducting sphere of 2.4 m diameter has a surfacecharge density of 80.0 μC/m2.(a) Find the charge on the sphere. (b) What is the total electricflux leaving the surface of the sphere?
(a) Diameter ofthe sphere, d = 2.4 m
Radiusof the sphere, r = 1.2 m
Surfacecharge density, 
=80.0 μC/m2 = 80 ×10−6 C/m2
Totalcharge 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 isgiven by the relation,
Where,
∈0= Permittivity of free space
= 8.854 × 10−12 N−1C2m−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.
(a) Diameter ofthe sphere, d = 2.4 m
Radiusof the sphere, r = 1.2 m
Surfacecharge density, =80.0 μC/m2 = 80 ×10−6 C/m2
Totalcharge 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 isgiven by the relation,
Where,
∈0= Permittivity of free space
= 8.854 × 10−12 N−1C2m−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.
