Question

A point charge causes an electric flux of -1.0x10 Nm /C to pass through a spherical Gaussian surface of 10cm
radius centred on the charge. (a) If the radius of the Gaussian surface were doubled, how much flux would
pass the surface ?
(b) What would be the value of point charge ? ​

Answer 1

answer : (a) -1.0 × 10³ Nm²/C (b) -8.854 nC

It has given that a point charge causes an electric flux of -1.0 × 10³ Nm²/C to pass through a spherical Gaussian surface of r = 10cm radius centred on the charge.

(a) electric flux is the ratio of charge enclosed the Gaussian surface to the permittivity of medium.

i.e., Φ = Q/∈_0

it is clear that electric flux doesn't depend on the radius of Gaussian surface.

so, electric flux remains same. i.e., - 1.0 × 10³ Nm²/C

(b) point charge inside the Gaussian surface, Q = Φ∈_0

= -1.0 × 10³ Nm²/C × 8.854 × 10¯¹² C²/Nm²

= -8.854 × 10^-9 C

= -8.854 nC