Why do 3 phase motors does not need neutral?

3 phase Motors are intrinsically balanced type of load when a motor is connected to 3 phase AC Power all of the phases will share the load equally. For the case of equal loads on each of three phases, no net current flows in the neutral. The neutral current is the inverted vector sum of the line currents. So we use 3 core cables and triple pole switch gears for 3 phase motors. Hence, there is no need of a neutral cable.

The three phase system provides three conductors, which have 120° out of phase voltage applied.

So if we consider phase A (say Red) to have the reference voltage on it (measured with respect to neutral for this description) then that voltage will climb to a maximum, drop down through zero and to a negative maximum, and then climb back up to maximum again, fifty times a second (or 60 in the USA et al).

The second phase B (say Blue) also has the same voltage, but it is delayed 120° in phase. This means that there is a voltage between Red and Blue which goes up to a maximum, down through zero, to maximum negative, then back up to maximum again, according to where in the cycle we are at any given time.

Sometimes Red phase and Blue phase will have the same voltage across them, for an instant, as Red is dropping and Blue is rising.

The third phase C (say Yellow or White) has its phase delayed by 240° from Red. So there is a voltage between all three conductors, which changes through out the cycle.

So for a load (say a three phase water heater), the three phases can provide a voltage difference between them, providing energy to heat the water. At some points in the cycle, current is flowing out of Red and into Blue while White is at zero. At other points, current flows out of Blue and into White, while Red is zero. At other points again, White sources current which flows into Red and Blue.

In this scenario a neutral connection is not required for transmission of power, as the three phases source and sink current according to where they are in the cycle.

A ground wire would be required for regulatory purposes (i.e. safety). But not for energy transmission.