A charge Q is situated at the centre of an imaginary hemispherical surface. By applying symmetry arguments and Gauss's law, determine the flux of the electric field due to this charge through the surface of the hemisphere, as depicted in the figure.

Step-by-step solution

According to Gauss's law, the total electric flux through a closed surface enclosing a charge Q is given by _ total = Q ₀ . To find the flux through the given hemispherical surface, imagine a complete sphere of the same radius with the charge Q at its center. The hemispherical surface forms exactly half of this complete spherical surface. By symmetry, the electric field lines emanate uniformly in all directions from the charge Q . Therefore, the electric flux through the hemispherical surface is exactly half of the