Question

A point charge q is at the point x = 0, y = 0, z = 0. An imaginary hemispherical surface is made by starting with a spherical surface of radius R centered on the point x = 0, y = 0, z = 0 and cutting off the half in the region z<0. The normal to this surface points out of the hemisphere, away from its center. Calculate the electric flux through the hemisphere if q = 3.00 nC and R = 0.100 m.

Answer 1

Ф = 54 Nm²/C

Step-by-step explanation:

We have point charge of 3.00 nC or 3.0 * 10⁻⁹ C

And distance of hemispherical surface to the charge point equal R

Then the flux through the surface 2πR² (hemispherical surface) is

Ф = ∫E*ds = E*2*π*R²

And Maxwell equation states E = Q/ ε₀

Therefore

Ф = Q/ ε₀ ( 2*π*R² ) Now we know K = 1/4*π*ε₀ = 9 * 10⁹ Nm²C⁻²

Ф = (1/2*π*ε₀)* (Q) Ф = (18 * 10⁹) * ( 3* 10⁻⁹) Ф = 54 Nm²/C