The method of images

The distribution of induced charges satisfies that condition. A way of avoiding the problem of calculating the ground plane charge distribution is provided by the method of images. Consider a vertical plane which is normal to the path taken by the overhead lines. The ground plane intersects this plane in a line which may be regarded as the x axis. The y axis then extends vertically upwards from the ground plane, with the origin immediately below the path of the lines (the exact location is irrelevant). Each line (which is typically a metallic conductor) intersects this vertical plane in a small circle (or some other figure, depending on the conductor shape).

In the method of images, the charges that are induced on the ground plane are removed. Image lines are then placed below the ground plane, exactly the same distance below the x axis as the actual lines are above it. Charges are placed on the image lines. They are constrained to be equal and opposite to the corresponding charges on the actual lines. Solving the field problem for this geometry automatically satisfies the required boundary condition that the field lines are vertical on the x-axis.