This is a very commonly discussed case in Electromagnetic Induction. In the case above, we need to find out the potential difference across the rod CD, in the presence of time-varying uniformly distributed cylindrical magnetic field as shown in the figure above.
Here we say that in equilibrium, the non-conservative electric field inside the rod completely balances the conservative electric field developed in rod, due to charge separation and the potential difference which we define in the ends of the rod, is due to the conservative electric field and not due to the non-conservative one, as there is no meaning of potential difference for non-conservative fields. I totally understand and agree with this explanation.
I do not have a doubt in the above case. The problem comes in the case below when we apply similar logic.
Consider case 2 above. Here we have a similar time-varying, uniformly distributed cylindrical magnetic field in the region as shown. An equilateral triangular conductor is placed in the magnetic field, with its centroid coinciding with the centre of the cylindrical region. The three branches of the triangle have the SAME resistances. In this case, we wish to find out the potential difference between the points A and B. This is a very common question given in the text-books.
My question is on this case 2.
In this case, we are asked the potential difference between points A and B.
We know that potential difference is a concept associated with a conservative electric field and not with the non-conservative one. Now in this case, how the conservative electric field will come into existence? The free charges inside the conductor will simply start moving just by the effect of the non-conservative induced electric field and there is no need for us to introduce a conservative electric field in this case like an isolated rod in case 1. And, if there is no conservative electric field then there is no concept of the potential difference!
By this logic, either the question itself is wrong, that it is asking for the potential difference between points A and B, in spite of having no existence of the conservative electric field,
OR I am missing something.
Kindly help me.
How do we understand the idea of potential difference in Case 2?
EDIT1: In the triangular conductor, I have changed the resistances of all the sides to be the same.