# What is the EMF in a bar rotating around any point?

The problem of a bar (or rod) of length $$l$$ rotating around one of its ends in a magnetic field of magnitude $$B$$ is very well known. The induced emf is $$\frac{1}{2}B\omega l^2$$, where $$\omega$$ is the angular frequency. And in the case where the bar is rotating around its center then the induced emf is $$\frac{1}{2}B\omega (\frac{l}{2})^2$$, which is the same voltage induced when a bar of length $$\frac{l}{2}$$ is rotating around one of its ends.

But my question is:

What is the induced emf when the bar is rotating around any other point inside the bar?

The research I have done so far:

The video Motional EMF and Rotating Rods says that it does not matter how many rods there are, as long as they are attached to the same central hinge, the induced emf (voltage) will be the same. The video also says that that happens because the two rods can be considered as two voltage sources connected in parallel.

The Quora post What would happen if two batteries connected in parallel says:

If the two cells connected in parallel are not identical, a few things can happen, as addressed in other answers. Firstly, the voltage of the cells will be balanced.

From that, my guess is that the axis (point) of rotation will move "automatically" to the middle of the bar, but this would generate other questions (which I can discuss in the comments/answers).

I would also like to know if anyone has found this exercise in any book. I have looked at Purcell's and Griffith's but have not found it there.

• What do you mean when you suggest that "the axis (point) of rotation will move automatically to the middle of the bar"? – sammy gerbil Dec 4 '18 at 1:40