At the ends of a half-wave dipole:

At the physical extremities of a half-wave dipole wire, there is nowhere else for the electrons to flow. Because the current cannot continue past the open end of the wire, the current distribution drops to its minimum (effectively zero). As the current reaches its minimum at the tips, the electrical potential difference (voltage) builds up to its maximum value. This combination of essentially zero current and peak voltage creates a very high impedance point at the antenna ends.