A hemisphere shell is uniformly charged positively. The electric field at a point on a diameter away from the centre (inside the boundary of hemispherical shell) is directed

A. perpendicular to the diameter

B. parallel to the diameter

C. at an angle tilted towards the diameter

D. at an angle away from the diameter

We have given that a hemispherical shell is uniformly charged with positive charge. We are asked to determine the direction of the electric field at a point on the diameter away from the centre. As the hemispherical shell is positively charged, the positive charge is present only on the outer surface of the hemisphere as the inner space of the hemisphere is hollow and empty.

Let us consider a test charge placed at a point P on the diameter of the hemispherical shell inside the boundary of the hemispherical shell.

Let us consider the electric field at point P due to the positive charges on the two edges of the diameter of the hemispherical shell. The direction of the electric field \[E\] at point P due to the positive charges on the edges of diameter of the hemispherical shell is as shown in the figure. The horizontal and vertical components of the electric field at point P are also shown in the figure.

From the diagram, we can conclude that the horizontal components of the electric field \[{E_x}\] at point P are parallel to the diameter of the hemispherical shell and directed opposite to each other. The vertical components of the electric field \[{E_y}\] at point P are in the direction perpendicular to the diameter and both the vertical components combine together to give the net electric field at point P on the diameter of the hemispherical shell. Therefore, the direction of the electric field at a point on the diameter away from the centre is perpendicular to the electric field.