Question

A point charge causes an electric flux of –6 × 10³ Nm² C⁻¹ to pass through a spherical Gaussian surface of 10 cm radius centred on the charge. 

(i) If the radius of the Gaussian surface is doubled, how much flux will pass through the surface? 

(ii) What is the value of charge? 

Answer 1

Given, φ = −6 × 10³ N m² C⁻¹ ; r = 10 cm = 10 × 10⁻² m

(i) If the radius of the Gaussian surface is doubled, the electric flux through the new surface will be the same, as it depends only on the net charge enclosed within and it is independent of the radius. 

∴ φ = −6 × 10³ N m² C⁻¹ 

(ii) ∴ φ = q/ε₀ or q = −(8.85 × 10⁻¹² × 6 × 10³) or q = − 5.31 × 10⁻⁸ C