What is the general definition of emf?

[kelvin490]

I have little problem in understanding emf in a circuit. There are three types of emf mentioned in textbooks and the first two are very similar:

1. The emf provided by a battery or other stationary power source. The emf is actually the voltage difference provided to the circuit.

2. The emf provided by a moving conductor in magnetic field.It is the work done to raise a charge to higher potential.

3. The work done to move a charge around a stationary loop encircled a changing magnetic field.

In the third case, the emf is defined as line integral of "E dot l" around a closed loop. However, in the second case, it doesn't make any sense to do the same integral around the circuit because in the moving conductor the force is magnetic but in the rest of the circuit the force is electrostatic in nature (because the charge accumulated on the two sides of moving conductor). So the line integral is only for the the part that is moving. It seems that there is a lack of general definition of emf because it different cases it means slightly different things. How to resolve this problem?

 

[Delta2]

Look at wikipedia, there the definition of the emf includes both the magnetic (the term v x B) and the electric force around a closed loop, as well as thermal and chemical forces. https://en.wikipedia.org/wiki/Electromotive_force#Formal_definitions_of_electromotive_force