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When a spring is kept in a magnetic field and current is passed through it, its edges act as parallel conductors and due to the action of Lorentz force, they pull themselves together. A spring contracts. As far as I know, magnetic field is non-conservative and cannot do work itself. i.e. It will only change direction of a moving body but never accelerate or decelerate it.

Then, from where does the elastic potential energy in the spring come from?

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  • $\begingroup$ Current going through the spring is extra energy. It creates magnetic dipoles, not only parallel conductors, and the dipole dipole interaction causing the contraction . $\endgroup$ – anna v Sep 20 '19 at 3:46
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The source of the elastic potential energy stored in the spring is the electrical power supply which you connected to the spring.
The energy from the power supply becomes energy stored in the magnetic field produced by the spring, the elastic potential energy stored in the spring as a result of its length contracting and energy dissipated as heat due to the circuit having resistance.
The magnetic fields interacting with currents (Lorentz) facilitate the described energy changes.
In a way the spring with an changing current passing through it acts as an electric motor converting electrical energy into mechanical energy.

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Magnetic force acting on conductor can do work on this conductor. This is because the conductor moves in the direction of the force.

The Lorentz force is the magnetic force acting on mobile charge carriers due to magnetic field and it is well known that it cannot do work on them.

But magnetic force acting on the conductor body is not those Lorentz forces. It is the sum of forces due to mobile charge carriers, pushing on the conductor. These are not the magnetic Lorentz forces, but internal forces between the mobile charge carriers and the rest of the conductor.

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