Conceptual difference between a motor and a generator

[greypilgrim]

Hi.

In order to explain the motion of an (accelerating) electromotor, we need the Lorentz force which itself is not one of Maxwell's equations.

Conversely, if we use the same electromotor inversely to generate electricity, Faraday's law (which is a Maxwell's equation) and the resistance of the circuit is enough to calculate the induced current, we don't need the Lorentz force law explicitely.

Those two processes look very symmetrical. But why do we need something beyond Maxwell's equations equation (namely the Lorentz force law) only when the device acts as motor? Or is the Lorentz force hidden somewhere (maybe in $I=U/R$ ?) when the device acts as a generator?

 

[Delta2]

The Lorentz force law is considered by many (and is also referred to as that in many books) to be the 5th Maxwell's equation. It is needed in order to explain the torque that causes the rotation of the motor. And no it is not hidden within Ohm's Law (Ohm's law in its differential form $\vec{J}=\sigma\cdot\vec{E}$ is unofficially the 6th Maxwell's equation).
EDIT: We can derive Ohm's law by using $\vec{F}=q\vec{E}$ and some other assumptions and using Newton's 2nd law, but the term $q(\vec{v}\times \vec{B})$ that appears in the full $\vec{F}=q(\vec{E}+\vec{v}\times\vec{B})$ Lorentz force law, has nothing to do with Ohm's law.

So basically, Maxwell's equations need to be packed with Ohm's law and Lorentz force law to explain fully operation of a generator and a motor. You need the Lorentz force law even in the case of generator , to explain the need for mechanical force that does mechanical work, in order to counter the Lorentz force and keep the generator at constant spin rate.

 

[Dale]

we don't need the Lorentz force law explicitely.

You do if you want to calculate the amount of mechanical force required.

But why do we need something beyond Maxwell's equations equation (namely the Lorentz force law) only when the device acts as motor?

You need it in both cases for a complete description of the device.

 

[A.T.]

Those two processes look very symmetrical. But why do we need something beyond Maxwell's equations equation (namely the Lorentz force law) only when the device acts as motor?

How we name and classify equations has often historical reasons rather than conceptual.