Question

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​

Answer 1

surface charge density of conducting sphere, $\sigma$ = 10 C/m²

we know, surface charge density is the rate of change of charge per unit area.

so, charge on conducting sphere, $Q=\sigma A$

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 ]