Class-12th Physics,
Electric Charges and Fields,
Chapter-1,Exercise -1, Q-1.22
NCERT Solutions for Class 12th Physics
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?
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Since diameter of the sphere, d = 4 m,
therefore Radius of the sphere, r = 1.2 m
Surface charge density, σ =80.0 µC/m2 = 80 x 10-6 C/m2
Total charge on the surface of the sphere,
Q = Charge density x Surface area = σ x 4 π r2 = 80 x 10-6 x 4 x 3.14 x (1.2)2 = 1.447 x 10-3 C Therefore, the charge on the sphere is 1.447 x 10-3 C.
Ans (b).
Total electric flux (ΦTotal ) leaving out the surface of a sphere containing net charge Q is given by the relation,
ΦTotal =Q/ε0
Where, ε0 = Permittivity of free space = 8.854 x 10-12 N-1C2 m-2
Q = 1.447 x 10–3C
Therefore ΦTotal =Q/ε0 = ( 1.447 x 10–3)/(8.854 x 10-12 )
= 1.63 x 108NC-1m2
Therefore, the total electric flux leaving the surface of the sphere is 1.63 x 108 N C-1 m2.