The voltage increase from some point  to some point  is given by
In this case, the voltage increase from point A to point B is equal to the work  done per unit charge, against the electric field, to move the charge from A to B without causing any acceleration.
Mathematically, this is expressed as the line integral of the electric field along that path.

Under this definition, the voltage difference between two points is not uniquely defined when there are time-varying magnetic fields since the electric force is not a conservative force in such cases.

If this definition of voltage is used, any circuit where there are time-varying magnetic fields, such as circuits containing inductors, will not have a well-defined voltage between nodes in the circuit.
However, if magnetic fields are suitably contained to each component, then the electric field is conservative in the region exterior to the components, and voltages are well-defined in that region.
In this case, the voltage across an inductor, viewed externally, turns out to be
despite the fact that, internally, the electric field in the coil is zero (assuming it is a perfect conductor).
The voltage increase from some point  to some point  is given by
In this case, the voltage increase from point A to point B is equal to the work  done per unit charge, against the electric field, to move the charge from A to B without causing any acceleration. Mathematically, this is expressed as the line integral of the electric field along that path. 
Under this definition, the voltage difference between two points is not uniquely defined when there are time-varying magnetic fields since the electric force is not a conservative force in such cases.
If this definition of voltage is used, any circuit where there are time-varying magnetic fields, such as circuits containing inductors, will not have a well-defined voltage between nodes in the circuit. However, if magnetic fields are suitably contained to each component, then the electric field is conservative in the region exterior to the components, and voltages are well-defined in that region. In this case, the voltage across an inductor, viewed externally, turns out to be
despite the fact that, internally, the electric field in the coil is zero (assuming it is a perfect conductor).
Voltage