1
$\begingroup$

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.

$\endgroup$
  • $\begingroup$ What do you mean when you suggest that "the axis (point) of rotation will move automatically to the middle of the bar"? $\endgroup$ – sammy gerbil Dec 4 '18 at 1:40
2
$\begingroup$

The induced EMF exists between the axis (stationary point) and the free end of the rod.

If two rods are joined to the same axis or hinge, then whether or not they are in the same straight line an EMF exists between the the axis and each free end.

In the same way, for a single rod with axis at its midpoint the free ends will be at the same potential difference relative to the midpoint. If the axis is not at the midpoint, so that one arm is longer than the other, the potentials at the two free ends will be different. They PD between the centre and each free end will be in proportion to the squared distances of the ends from the axis.

$\endgroup$

Your Answer

By clicking "Post Your Answer", you acknowledge that you have read our updated terms of service, privacy policy and cookie policy, and that your continued use of the website is subject to these policies.

Not the answer you're looking for? Browse other questions tagged or ask your own question.