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Electromagnetic induction sounds quite analogous to inertia to me. Just like inertia it opposes the 'change'.

So is this phenomenon has something to do with what we call inertia for macroscopic objects. And do electron has some inertia like property to create this phenomenon.

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The reason that the induced current opposes the change in magnetic flux is so that energy will be conserved. You can see this mathematically by the minus sign in Faraday-Lenz law:

$$\epsilon = \int \vec E \cdot d\vec s = - \frac{d\Phi_B}{dt} $$

Think about it the other way. If the induced current increased the magnetic flux, that would increase current, which would increase the flux again, and increase the current, and so on. So the current would continually increase and we would have free energy! Unfortunately, this doesn't happen because of conservation of energy.

That said, it is quite analogous. The electrons are flowing at some current $I=dq/dt$. The electrons have a net velocity or "drift velocity" when the potential difference and electrical resistance are held constant. So, if we induce a current to oppose the change in flux, we change the voltage and therefore can cause the electrons to accelerate. The electrons will want to persist in uniform motion.

I should disclaim that this idea works if we treat electrons as classical objects, but my answer here probably does not hold in quantum electrodynamics or any modern field theories.

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Here is one interesting idea that links inertia with Unruh radiation and a Rindler Event Horizon

The property of inertia has never been fully explained. A model for inertia (MiHsC or quantised inertia) has been suggested that assumes that 1) inertia is due to Unruh radiation and 2) this radiation is subject to a Hubble-scale Casimir effect. This model has no adjustable parameters and predicts the cosmic acceleration, and galaxy rotation without dark matter, suggesting that Unruh radiation indeed causes inertia, but the exact mechanism by which it does this has not been specified. The mechanism suggested here is that when an object accelerates, for example to the right, a dynamical (Rindler) event horizon forms to its left, reducing the Unruh radiation on that side by a Rindler-scale Casimir effect whereas the radiation on the other side is only slightly reduced by a Hubble-scale Casimir effect. This produces an imbalance in the radiation pressure on the object, and a net force that always opposes acceleration, like inertia. A formula for inertia is derived, and an experimental test is suggested.

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