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I have been trying to understand antennas and I've been trying to analyze how the transmitter's energy is transferred. It is clear that for current to flow there must exist a potential difference across two points. The accelerated charge (current) that is produced will then radiate EM waves. In the case of a dipole antenna as depicted here at Wikipedia there is an AC source but it is only attached to the ends of the wires with no electrical connection between them, and the animation shows the ac current when there should not be any since no potential exists.

If I continue with this logic, I become confused when I consider the scenario where there is a current carrying wire and I stood on a plastic stool and touched the wire does it mean that current will flow to me as well even though I am at the same potential as the wire?

The mechanical analogy I have in mind is that of a bowling ball that has been laid on a shelf where it rests with some potential energy, and in order to convert this energy into kinetic energy the ball would need to be dropped. This symbolizes the potential difference that the wires must have in order to allow charge to flow (ball to be dropped) and thus transmit energy.

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The rule that says a wire has the same potential at every point is a rule for lumped circuits. The lumped circuit approximation applies when the dimensions of the circuit are much smaller than the wavelength associated with the frequencies of the signals present. An antenna, on the other hand, typically must have a dimension that is a substantial fraction of the wavelength, for example 1/4 or 1/2 wavelength. Therefore an antenna is, practically by definition, not a lumped circuit, so that rule doesn't apply.

In fact there will be a potential difference (disregarding the fact that you have to be careful about even using the concept of potential in a distributed circuit) between the points along the antenna, which pushes the charge around and produces the radiation.

the animation shows the ac current when there should not be any since no potential exists.

The red curve in the animation shows how the potential varies along the antenna. It shows there absolutely is a potential difference between different locations along the antenna.

It is true that the potential difference goes to zero at the instant when the currents are at a maximum, and vice versa. This phase difference comes about because the antenna has both inductance and capacitance, and again because the dimensions of the antenna are on the same order of magnitude as the wavelength of the signal.

I become confused when I consider the scenario where there is a current carrying wire and I stood on a plastic stool and touched the wire does it mean that current will flow to me as well even though I am at the same potential as the wire?

The current flowing to you is why you reach the same potential as the wire. Before you touched the wire you were at some other potential. When you touched it, some charge flows in to (or out of) your body to the wire, and that is why you achieve the same potential as the wire.

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I think you look at this with too much dc sight in your mind. A dipole antenna is like a small c-l-c-l.... strip. You have a capacitor from one end to the other end and in series the inductivity.

So now, when you charge the antenna there is a current flow through the L part of the antenna and a B field. If the current stops; at this moment you have a voltage at the end and a potential (90° behind the current), which gives the E part of the field. This is happening so fast, that the voltage across the antenna has different values (as it is supposed to be). So through the fast changing signal you have a current flow and through the current flow and the c-l characteristic a phase of 90°.

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