Question

curl of magnetic flux density is not zero what is the conservative?​

Answer 1

Answer:

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Answer 2

Answer:

Is magnetic field conservative or non-conservative?

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The magnetic field is non- in a metaphorical/technical sense which is a bit of a misnomer.

The original notion of conservative is that a field is conservative when the force on a test particle moving around any closed path does no net work. Electrostatic and gravitational fields are conservative in this sense. The mathematical underpinning which justifies persisting with the term in other contexts is that a electrostatic of gravitational field can be derived as the derivative of a scalar potential function. For conservative fields that exert forces directly on charges, the physical interpretation of the potential function is the energy of a charge as a function of position in the field (and scaled by the charge), and the fact that it is well-defined means that the energy has to be the same after going for a journey and returning to the same point - i.e., the energy is conserved.

But magnetic fields only act on moving charges, and at right angles to the motion, so the work is always zero and the concept doesn't properly apply.

Of course, if there were magnetic monopoles, they would try to follow the magnetic field the way electric charges try to follow the electric field lines. And since magnetic field lines can only go in closed paths, that would create a non-conservative force on the monopoles. So the magnetic field is described as non-conservative, even though the original intuition doesn’t quite apply - there are no magnetic monopoles as far as we know or suspect.

So not only doesn’t the label apply literally, for lack of magnetic monopoles, it doesn’t even apply in the mathematical sense, because the magnetic field can’t be derived from a scalar potential.

Mind you, the magnetic field can be derived from a vector potential function, and this underlies the fact that if you have a test magnetic dipole in a magnetic field, e.g., a small permanent magnet, which simulates an opposed pair of magnetic monopoles, the energy is a well-defined function of position and orientation of the dipole. But that’s not what’s usually regarded as conservative.