14.
AIIMS 2010
A charged conducting sphere has diameter 2.4 m
and surface charge density 10 C/m². Electric flux
passing through its surface will be :-
(1) 2 x 107 Nm²/C (2) 16 x 107 Nm²/C
(3) 1 x 106 Nm²/C (4) 2.2 x 108 Nm²/C
Answers
surface charge density of conducting sphere, = 10 C/m²
we know, surface charge density is the rate of change of charge per unit area.
so, charge on conducting sphere,
where A is area of conducting sphere,
A = 4πr² , given 2r = 2.4 m
so, A = 4π × (1.2)² = 5.76π m²
now, charge on conducting sphere, Q = 10C/m² × 5.76π m² = 57.6π C
electric flux is the ratio of charge enclosed inside gaussian surface to the permittivity of medium.
value of permittivity in vaccum is 8.85 × 10^-12 C²/Nm²
so, electric flux = 57.6π/(8.85 × 10^-12)
= (57.6 × 3.14/8.85) × 10¹² Nm²/C
= 20.43 × 10¹² Nm²/C
= 2.043 × 10¹³ Nm²/C
[ note :- here answer is different because your given data must be different with actual data. well it's okay. you just use to find electric flux by using above concept ]