We know by Faraday's law that emf induced in a closed coil is given by the negative rate of change of magnetic flux associated with the coil....but is the induced electric field set up in any coil due electromagnetic induction always non conservative....for example, the one setup due to self induction or due to mutual induction?

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    \$\begingroup\$ What specifically do you mean by non conservative? \$\endgroup\$ – Andy aka Apr 7 '17 at 17:37
  • \$\begingroup\$ That the work done on a charged particle by the field as it moves in a closed loop is not zero \$\endgroup\$ – user372205 Apr 7 '17 at 17:40
  • \$\begingroup\$ @user372205 Not sure of your context, because you don't mention what else is going on around all this, but the work done is typically supplied by an energy source in electric/electronic circuits. I think you need to completely elaborate the situation, in detail. \$\endgroup\$ – jonk Apr 7 '17 at 17:43
  • \$\begingroup\$ @jonk There isn't any specific scenario that I am enquiring about .I am asking that is the induced electric field in a closed coil due to the change in the magnetic flux associated with it, is always non conservative?For example, let us imagine a closed circular loop of a wire such that a magnetic flux B is associated with it.Now as this flux B changes, an electric field is setup in the wire which gives out an effective emf. Is this electric field non conservative. \$\endgroup\$ – user372205 Apr 7 '17 at 17:55
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    \$\begingroup\$ I'm voting to close this question as off-topic because it belongs in Physics, not Electrical Engineering. \$\endgroup\$ – Robherc KV5ROB Apr 10 '17 at 6:06

An electric field will be conservative or not depending on its curl

A field with zero curl can be made with an arrangement of electrodes. If you take a point charge, it will gain and lose energy as you move it around. However, if you take it on a closed loop, the energy will be the same before and after the transit round the loop. The potential energy of the point charge at some location is another way of defining the electrical potential there.

A field with non-zero curl can be made by having an area of changing magnetic flux through it. If the loop path taken by the point charge misses the area of flux, its movement will be conservative. If the loop path encircles the flux, then its movement will be non-conservative, it will gain or lose energy in the motion. If the point charge makes several rotations around the flux, it will change energy each time it passes round. The potential of the field in this case is multi-valued, depending on how many times we have been round the flux.

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  • \$\begingroup\$ Yes, that is what I am asking. Is the electric field in closed loop generated due to the changing magnetic flux through the loop always non conservative. \$\endgroup\$ – user372205 Apr 7 '17 at 19:10
  • \$\begingroup\$ The energy of a point charge always changes when it circles the changing flux, so yes, if by non-conservative you mean gains or loses energy. In my dim'n'distant past, I recall our definition of non-conservative was that the change of energy going round a closed path depended on the path taken. By that definition, the change in energy is different depending on whether the path encloses the changing flux or not. Exactly the same argument. \$\endgroup\$ – Neil_UK Apr 7 '17 at 19:15
  • \$\begingroup\$ Thanks for the explanation. And just one more thing, what do you mean when you say - If the loop path taken by the point charge misses the area of flux, its movement will be conservative. \$\endgroup\$ – user372205 Apr 7 '17 at 19:27
  • \$\begingroup\$ You already know what I'm attempting to say. As I'm not a student of topology, so not ready to trot out technical terms, and can't be bothered to draw a diagram, I' trying to convey the concept of 'winding number', how many times a conductor gets looped round a bundle of changing flux, and whether a loop links another loop. If the loop does not link the flux, then the potential is uni-valued, and the path taken does not change the energy. If the loop does link the flux, the potential is multi-valued, and the change of energy depends on the angle through which the charge moves wrt the flux. \$\endgroup\$ – Neil_UK Apr 8 '17 at 2:44

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