A point charge q is placed at the centre of the hemispherical surface of radius R. The flux through the hemispherical surface is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \( \displaystyle\frac{q}{2\varepsilon_0} \)
Complete the hemisphere into a full sphere of the same radius with the charge at its centre. By Gauss’s law the flux through the whole sphere is \( q/\varepsilon_0 \).
By symmetry the field is the same at every point of the sphere, so the flux divides equally between the two hemispheres.
\( \displaystyle \phi_{\mathrm{hemisphere}} = \frac{1}{2}\times\frac{q}{\varepsilon_0} = \frac{q}{2\varepsilon_0} \)