What factors affect induced voltage and how is it calculated?

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Discussion Overview

The discussion revolves around the factors affecting induced voltage in a circuit and the calculation methods involved. Participants explore the implications of nonconservative electric fields, the definition of voltage between points, and the role of magnetic flux and circuit components in determining induced emf.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant expresses confusion about the definition of voltage in a nonconservative field and questions the clarity of the problem statement.
  • Another participant suggests that induced voltage can be represented as dφ/dt, seeking clarification on whether more information is needed.
  • A different participant reflects on the traditional method of calculating voltage as the work done to move a charge, noting the ambiguity in the current context.
  • It is mentioned that if the magnetic field (B) is constant, a change in the area of the loop is necessary to induce emf.
  • One participant asserts that the relationship of resistances in the loop components may influence the solution.
  • Another participant clarifies that the emf is independent of resistance, as it is derived from the contributions of each segment of the wire, and discusses the potential complications in measuring emf due to circuit routing.
  • Reference is made to a previous discussion and a lecture by Walter Lewin that addresses related paradoxes in the context of induced voltage.

Areas of Agreement / Disagreement

Participants express differing views on the clarity of the problem and the factors influencing induced voltage. There is no consensus on the best approach to calculate the induced voltage or the implications of resistance in the circuit.

Contextual Notes

Participants note the ambiguity in defining voltage in a nonconservative field and the potential for confusion arising from circuit diagrams. The discussion highlights the complexity of induced voltage calculations and the varying interpretations of the problem.

Fibo112
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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.
 

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Isn't it just dφ/dt?
That's my first thought on the matter. Are you looking for more than that?
 
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
 
Fibo112 said:
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.
 
sophiecentaur said:
If B is constant then it is necessary for the loop to change area if you want to induce an emf.
this I know
 
wouldn't the solution here depend the relationship of the resistances of the different components of the loop?
 
Fibo112 said:
this I know
I thought you did but your comments made me wonder.
Fibo112 said:
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.
 

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