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Hello everyone.

The definition of EMF, given in "Introduction to Electrodynamics" by David J. Griffiths, is the line integral of force per unit charge around a closed path in the circuit. However, it's pretty clear that this definition is suitable only for infinitely thin wires, in which only one path is possible. For situations in which several (or an infinite number of) paths are possible (e.g. a wire with non-zero diameter), what should be done? Is it some sort of averaging (like integrating EMFs of different paths over the wire's cross section and dividing it by the area)?

Same question arises in case of a Faraday wheel rotating in a non-uniform magnetic field, which would make the EMF integral path-dependent, and this can't be ignored since we know that in this device, the current is somehow distributed throughout the rotating disk, and when the field is uniform, the EMF becomes path-independent.

Any answers would be appreciated.

Regards,

Martinius

EDIT: I understand that as wire thickness increases, Eddy currents resulting from unevenly distributed force per unit charge (and therefore EMF) become more significant, but I'm interested in a more quantitative discussion of these currents and their effect on the overall EMF which generates a current in the entire circuit.

The definition of EMF, given in "Introduction to Electrodynamics" by David J. Griffiths, is the line integral of force per unit charge around a closed path in the circuit. However, it's pretty clear that this definition is suitable only for infinitely thin wires, in which only one path is possible. For situations in which several (or an infinite number of) paths are possible (e.g. a wire with non-zero diameter), what should be done? Is it some sort of averaging (like integrating EMFs of different paths over the wire's cross section and dividing it by the area)?

Same question arises in case of a Faraday wheel rotating in a non-uniform magnetic field, which would make the EMF integral path-dependent, and this can't be ignored since we know that in this device, the current is somehow distributed throughout the rotating disk, and when the field is uniform, the EMF becomes path-independent.

Any answers would be appreciated.

Regards,

Martinius

EDIT: I understand that as wire thickness increases, Eddy currents resulting from unevenly distributed force per unit charge (and therefore EMF) become more significant, but I'm interested in a more quantitative discussion of these currents and their effect on the overall EMF which generates a current in the entire circuit.

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