The hemisphere shown below is positively charged. There are infinite numbers of diameters passing through the centre of the hemisphere. Consider any one of the diameter say PQ as shown in the figure below. Now consider electric field at a point P which is away from the centre. There are two components of electric field shown in the figure, one is parallel component () parallel to the diameter and the other is perpendicular component () perpendicular to the diameter. Similarly, there are parallel and perpendicular components of electric field at the point Q.

The parallel components of electric field at point P and Q have opposite direction and thus cancel each other. Only perpendicular components of electric field remains and they add up to each other.

If we now consider such infinite diameters, all the perpendicular components add up to each other while parallel components cancel each other. Therefore, the electric field at a point away from the centre is directed perpendicular to the diameter.