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We explain that motional emf is induced because charges in a conductor move along with the conductor and as a result a magnetic force pushes them to one side of the conductor. But in case of a stationary conductor with v=0 how can variable magnetic field apply force on stationary charges inside a stationary conductor? If we say charges (electrons in this case) are in random motion so they undergo magnetic force, in such case , constant magnetic field should also induce emf? Thanks if u answer my question.

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  • $\begingroup$ This question has always worried me when I teach my K-12 class. $\endgroup$ – Zahid Iftikhar Ahmad Aug 11 '14 at 18:25
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For the stationary case with time varying magnetic field Maxwell's equations produce an induced electrical field which will accelerate charges. For the case of moving conductor and stationary field, a Lorentz transform of the constant magnetic field into the frame of the moving conductor will, again, produce an induced electrical field. In both cases the forces on charges are caused by the electric field component.

A constant magnetic field in the coordinate system of moving charges will therefor always produce an effective electric field component, which will result in an acceleration of charged particles. This can be shown very nicely in experiments, in which electron beams get deflected by a constant magnetic field.

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But in case of a stationary conductor with v=0 how can variable magnetic field apply force on stationary charges inside a stationary conductor?

$$\nabla \times \vec E = -\frac{\partial \vec B}{\partial t}$$

$$\vec F = q(\vec E + \vec v \times \vec B)$$

There is a non conservative electric field associated with a time changing magnetic field and thus, a force on the charge carriers in the conductor.

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