When a Conducting charged circular loop is placed in a linearly varying magnetic field, will the loop start rotating or current will flow along the loop or both ? Here the plane of the loop is perpendicular to magnetic field and the magnetic field is present cylindrically and coaxial with the circular loop.[the induced electric field near the loop is tangential to the loop][
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$\begingroup$ This is how transformers work, as well as the dynamic on a bike. $\endgroup$– my2ctsCommented May 8, 2020 at 20:16
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In this particular case, the electromotive force would be the time derivative of the flux, $$\cal{E} \propto - \frac{\partial \Phi}{\partial t},$$ where you can set $\Phi = \pi \, r^2 \, B_{0_x} \, t.$ taking the radius of the inner circle as $r.$ You would also notice that the force on the charges in this current experiment a force which is radial $\vec{F} = q \vec{v} \times B_{0_x}$ and would not make the inner loop rotate. This new current would create a magnetic field on the exterior loop and would again cause a current there. However, due to Lenz's Law this new current would decrease $B$ in the inner circle. This mutual inductance can be calculated, I have no idea if this is what you want from your question.
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$\begingroup$ At molecular level since number of electrons is not equal to number of protons and induced electric field is tangential to the loop there will be non zero torque which will cause the loop to rotate, is my analysis correct? $\endgroup$– vangalaCommented May 10, 2020 at 2:34
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$\begingroup$ The electric field would cause a current with or without and excess charge in a conductor in your example. However, even though that current (moving charges) in a magnetic field would experience a force, the torque is null because for the case the force is in the same plane as the loop. $\endgroup$ Commented May 10, 2020 at 14:25