Currents on the surface of an infinite cylinder excited by an axial slot
especially when the end surfaces are rigorously treated. However, if the slot is situated half way between the ends of the cylinder, the peripheral surface current distribution and the radiation pattern in the plane through the slot and perpendicular to the axis of the cylinder is approximately the same as for an infinite cylinder with an infinitely long axial slot. Therefore, in so far as this peripheral surface current and radiation pattern is concerned, it is only necessary to solve the following problem. The problem investigated is the distribution of currents on the surface of an axially infinite cylinder of radius a fed from an axial slot across which is maintained a constant distribution of electric field defined by