Current element and λ/2 antenna
Some guidance: Your antenna is NOT a current element, a half-wavelength dipole must be considered to have non-uniform current distribution. The current element far-field H formula must be integrated - a highly complex task, but well presented in antenna theory books. It's complex because all current elements have different phase angles and the current distribution function isn't simple. Sinusoidal distribution is often used approximation, but it's far from accurate.
I guess you should forget current element radiation integration and use antenna handbooks to find the gain of your dipole. With radiation resistance you calculate the radiated power and find the intensity (watts/sq.meter) at the wanted distance with the gain factor. The gain becomes from the directivity, it doesn't increase energy.
From intensity you calculate E and H as rms values. Their product E*H is the radiation intensity. E and H in free air and far away from the antenna have ratio 377 Ohms. H and E are perpedicular, have the same phase angle and E is in parallel with the dipole.