Definition of induced voltage

[Fibo112]

I am asked to caluculate the induced voltage between the two sides. To me it is confusing what is meant since the field is nonconservative. Is the question phrased in an unclear way or am I missing something about the actual definition of the voltage between two points.

 

[sophiecentaur]

Isn't it just dφ/dt?
That's my first thought on the matter. Are you looking for more than that?

 

[Fibo112]

Maybe I was just overthinking it. Usually when I want to figure out the voltage between two points I calculate the work needed to move a charge from one point to the other. Since this is not well defined here I was unsure how to proceed. I guess here since there is only one closed circuit they are talking about the work done when traveling once around this circuit, which is well defined.

edit: they are not asking for the emf for one loop but for traveling from one side to the other, I have to think on this some more

 

[sophiecentaur]

for traveling from one side to the other,

If B is constant then it is necessary for the loop to change area if you want to induce an emf.

 

[Fibo112]

If B is constant then it is necessary for the loop to change area if you want to induce an emf.

this I know

 

[Fibo112]

wouldn't the solution here depend the relationship of the resistances of the different components of the loop?

 

[sophiecentaur]

this I know

I thought you did but your comments made me wonder.

wouldn't the solution here depend the relationship of the resistances of the different components of the loop?

The emf is the open circuit volts so resistance doesn't come into it. Each elemental bit of the wire produces a small emf and they all add up to the point ( gap) of interest in the circuit.
I think the original diagram is a bit sloppy (as is common with such diagrams. The emf, measured with two wires to a meter, will depend on the routing of the wires and there are a number of apparent Paradoxes that turn up concerning this. I think that the dφ/dt would be enough to be getting on with here. It's the flux through the area to the right hand side of the grey bar that counts.

There was a thread about this not long ago. You could search for it. There's a Movie of a lecture by Walter Lewin which deals with the apparent paradox.