Ground loop explanation: the failure of the "potential" concept
Ground loops develop even when shielding, twisted pairs, and coaxial cables are used. Ground loops are sometimes ascribed as being caused by two different circuits having different "ground potentials" but this explanation is incorrect because the concept of potential becomes inadequate when time-dependent magnetic fields exist. This inadequacy can be demonstrated by the following simple experiment. When the leads of a voltmeter are connected between two points in a DC circuit, the meter voltage depends on the respective contact points of the two leads but not on the physical arrangement of the leads. If contact point of lead #1 is held fixed while contact point of lead #2 is moved, the voltage measured at each contact point position of lead #2 can be characterized as a potential associated with the contact point. However, this procedure fails when time-dependent magnetic fields exist, because the voltmeter reading is seen to depend on the lead layout even though the lead contact points are held fixed. Because no unique voltage difference between two contact points can be determined, it is incorrect to state that a potential difference exists between these contact points.
The above measurement ambiguity results because the amount of magnetic flux linked by the meter leads depends on how they are arranged despite their points of contact being fixed. The definition of electric field, namely force per unit charge, does not assert that electric field is given by a potential drop. In fact, electromagnetic theory shows that an electric field can be created in two distinct ways: (i) by a gradient in electrostatic potential or (ii) by a time-varying magnetic field. A type (i) electric field is called a potential or electrostatic electric field while a type (ii) electric field is called an inductive electric field. Ground loops are associated with type (ii).
Electrostatic electric fields, the type responsible for capacitive coupling, have the property of being "conservative". A familiar example of a conservative field is gravity. Gravity being conservative means that when a person climbs to the top of a frictionless hill and then returns to the starting point following any path, the net work done by the person is zero. Climbing involves the person doing work against gravity while on descent gravity does an equal amount of work on the person so the person does no net work on completing the round trip. The altitude at any point represents the potential energy available on descent and is an exact analog to electrostatic potential. Presumption that a potential energy exists is essentially an assertion that the electric field is conservative and obeys Kirchoff's voltage law. If the electric field is non-conservative, Kirchoff's law does not apply.
As an example of a non-conservative field, consider a person walking into a headwind which then reverses direction when the person reverses direction and returns to his/her starting point. In contrast to the situation described in the previous paragraph, here the round-trip net work done by the person is both finite and path-dependent. Because the energy available to the person cannot be expressed in terms of the person's position, the system is non-conservative. The part of an electric field produced by a time-dependent magnetic field has this non-conservative, path-dependent, non-potential nature. A new quantity, the loop voltage Vloop, can be defined to characterize this non-potential situation. The loop voltage is the amount of work done on going once around a circular path.
Kirchoff's law, an assertion that Vloop is zero, is valid for DC circuits but is superseded by Faraday's law when the circuit is AC. Faraday's law states that Vloop = - dF/dt where F= is the magnetic flux linking the loop. The magnetic flux is given as F=BA where B is the magnetic field linking the loop and A is the loop area. Faraday's law is the basis of transformers and inductors. Ground loops depend on Faraday's law but have two distinct behaviors depending on frequency; understanding these behaviors requires understanding the resistance and inductance associated with the ground loop.