Examine Maxwell's equations and read about them. Changing electric fields generate magnetic fields perpendicular to them. Sometimes the magnetic and electric fields are not in phase with each other. When they are in phase they carry energy, as radiation, or in a transmission line, for example.
Relativity shows that magnetic fields are the difference between electric fields of objects moving at different speeds (for instance the moving electrons in a wire and the non-moving positive charges).
I believe that in a resonant half-wavelength dipole antenna the voltage is maximum at the ends and minimum in the center. The current is maximum at the center and minimum at the ends. Another way to think about this is that a half-wave antenna, when excited by an RF source, produces an oscillation of the free electrons in the wire. Since the electrons pile up at the ends, the maximum "charge" or voltage occurs at the ends. When the electrons move from one end of the antenna to the other, the greatest number of them move past the center so the center has maximum current flow. And because the electrons that pile up at the end can't move past the end, there is zero current at the ends. When the electrons pile up at the far ends, voltage at the ends is maximum and current is zero. When the current at the center is maximum, the voltage at the ends is zero. This is the same 90° voltage and current phase relationship that occurs in any freely oscillating inductor-capacitor circuit.
Electrical and magnetic fields are not combining at antenna to form electromagnetic radiation.
Variable currents are sources of Hertz magnetic transverse radio waves. Electric field is not here. Variable charges are sources of Tesla electric longitudinal waves. There is no magnetic field in them. The interconversion of electric and magnetic fields is a myth. If you find the time and desire to understand everything, read my book "Electromagnetic Gravity. Part 3" in my profile.
Add the Biot-Savart Law (Ampere's) part of Maxwell's Equations calculate the magnetic field around the current carrying conductor. The STOE suggests photons are magnets which are ejected from the current. The movement of these small magnets induce the electric field effect of EM signals and the speed of the photons (speed of light) is the speed on EM signals. BUT note the speed of coulomb fields has been measured (de Sangro) as many time the speed of light. So, EM signals cannot be electric field inducing magnetic field.