A point charge causes an electric flux of –1.0 × 10³ Nm²/C to pass through a spherical Gaussian surface of 10.0 cm radius centred on the charge. (a) If the radius of the Gaussian surface were doubled, how much flux would pass through the surface? (b) What is the value of the point charge?

Given:

Φ = -1.0 × 10³ Nm²C^-1

r₁ = 10.0 cm.

a) Flux if the radius of the Gaussian surface is doubled.

If the radius is doubled then the flux would remain same i.e. -1.0 × 10³ Nm²C^-1_.

The geometry of the Gaussian surface doesn’t affect the total flux through it. The net charge enclosed by Gaussian surface determines the net flux.

b) Let value of point charge enclosed by Gaussian surface = q

We know that,

Flux, Φ = q/ε₀ …(1)

Where, q = net charged enclosed

ε₀ = permittivity of free space

ε₀ = 8.85 × 10^-12N^-1 m^-2C²

Now plugging, the values Φ and ε₀ in equation (1).

q = Φ × ε₀

⇒ q = -1.0 × 10³Nm²C^-1 × 8.85 × 10^-12N^-1m^-2C²

⇒ q = -8.85 × 10^-9 C

The charge enclosed by the surface is -8.85 × 10^-9 C.