A light straight slider $$1$$ m long can slide over two straight long parallel rails, vertically kept. when a uniform magnetic field of $$0.6$$ T is applied perpendicular to the plane of rails, the slider is found moving with a constant velocity.At this instant power dissipated in rails and slider due to their resistance is $$1.96$$ W. If slider has a mass of $$0.2kg$$, then the terminal velocity of the slider is $$________$$.

Question

A light straight slider $$1$$ m long can slide over two straight long parallel rails, vertically kept. when a uniform magnetic field of $$0.6$$ T is applied perpendicular to the plane of rails, the slider is found moving with a constant velocity.At this instant power dissipated in rails and slider due to their resistance is $$1.96$$ W. If slider has a mass of $$0.2kg$$, then the terminal velocity of the slider is $$________$$.

Infinity Learn · Accepted Answer

Let v be the terminal velocity of the slider then, emf developed $$=e=Blv$$ Power dissipated will be $$P=i2R=eR2$$⋅$$R=eiWhen$$ slider achieve terminal velocity, net downward force on slider is zero.Or magnetic force $$=$$ gravitational force⇒ $$Bil=mg$$⇒ $$i=mgBl=0.2$$×$$9.81.0$$×$$0.6=3.27A$$ As power developed $$P=ie$$⇒ Emg induced, $$e=Pi$$⇒$$e=1.963.27=0.6V$$ But $$e=Blv$$⇒$$v=eBl=0.60.6$$×$$1.0=1ms$$−$$1$$

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