# Hall effect over a conducting ring

Trisztan
Homework Statement:
What is the voltage around a conducting ring of diameter ##l##, moving through a uniform magnetic field of magnitude ##B##, at speed ##v##?
Relevant Equations:
Definition of potential difference:
$$\Delta V = -\int_i^f {\mathbf{E}\cdot \mathrm{d}\mathbf{s}}$$
Force magnitude equivalence under the Hall effect:
$$qE = qvB$$
This is the diagram provided in the question:

The ring is made of conducting material. I was originally asked to find the potential difference between ##a## and ##b##. I did so using the Hall effect (and assuming it would work as per normal in this situation). This got me ##\Delta V = vBl##.

However, I am now lost on how to find the "voltage around the ring". If I had to guess, I would say its 0 everywhere around the ring except at either ##a## and ##b## (depending on which you take to be the point where ##V=0##).

Any help would be much appreciated.

Homework Helper
Gold Member
You need to do a line integral $$\int_a^b \mathbf{E}\cdot d\mathbf{s}=\int_a^b (\mathbf{v}\times \mathbf{B})\cdot d\mathbf{s}$$ where ##d\mathbf{s}## is a line element along the circular path.

Trisztan
@kuruman Sorry, but I don't understand how that will help me. Wouldn't that just give me ##-\Delta V## between ##a## and ##b##? I already have that, don't I?