A point charge causes an electric flux of -2 × 10⁴ Nm² C⁻¹ to pass through a spherical Gaussian surface of 8.0 cm radius, centred on the charge. The value of the point charge is :
(Given ε₀=8.85 × 10⁻¹² C² N⁻¹ m⁻² )

Solution

Physics sir · 4 steps

Gauss's law gives charge = flux times epsilon-nought, and the radius of the sphere does not matter.

1. Gauss's law. The total flux through any closed surface depends only on the charge enclosed. The size and shape of the surface do not enter, so the 8.0 cm radius is extra information.

   φ = q/ε₀ ⇒ q = φ ε₀

2. Put in numbers. q = (-2 × 10⁴) × (8.85 × 10⁻¹²) = -17.7 × 10⁻⁸ C.
3. Read the sign. Negative flux means the field lines point into the sphere, which is what a negative charge produces.
4. So. The point charge is -17.7 × 10⁻⁸ C, option (b).

The idea to keep. Flux through a closed surface depends only on the enclosed charge, not on the surface's size or shape. Keep the sign of the flux, because it tells you the sign of the charge.

Answer from the NTA final answer key. Solution by PrepWiser.