On the electric charge collected by water drops falling through ionized air in a vertical electric field

Abstract

In connection with the theory of thunderclouds and of the electric charge brought down by rain, Wilson has suggested* the following mechanism. Consider an uncharged water drop falling vertically through ionized air. Let there be a vertical electric field, so that ions of one sign are moving down in the same direction as the drop falls, while ions of the other sign are moving up against the drop. The electric field induces equal charges of opposite signs on the upper and lower halves of the drop. Suppose now that the electric field has such an intensity that the velocity of the descending ions is less than the velocity of the falling drop. Under these conditions those descending ions which arc above the drop, cannot overtake the drop and so do not reach it, although attracted by the charge on its upper half. Those descending ions which are below and which the drop overtakes, are first repelled by the lower charge on the drop before being attracted by the upper charge and, since these charges are equal in the neutral drop, it is to be expected that these ions will not reach it. Ions coming up to meet the drop are attracted to the lower charge and give the drop a net charge. This destroys the equality of the induced charges and some of those ions which the drop overtakes are now attracted to it. A limiting condition will be approached in which the net charge is equal to some fraction of the induced charge. This mechanism does not depend on whether the electric field is directed vertically upwards or vertically downwards and for this reason specific mention of the sign of an ion has been avoided. In a particular case, suppose the potential gradient, measured upwards, to be negative, so that positive ions move up and negative ions move down. The charges on the upper and lower halves of the falling drop will then be positive and negative respectively. If the water drop falls more rapidly than the negative ions move down, it will collect a net positive charge, by selective absorption of positive ions at its lower negatively charged surface. Since a drop of 1 mm. radius has a terminal velocity of about 6 metres per second, the electric field must not exceed 400 volts/cm. for ions of mobility 1·5 cm./sec./volt/cm.