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Titan97
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Homework Statement
A conduction rod (of mass ##m## and length ##l##) was placed on two smooth conducting rails rails connected by a resistor as shown: (the circuit is placed in ##XY##-plane
A constant uniform magnetic field is switched on along ##-Z## direction with magnitude ##B##
The rod is given an initial velocity ##u##. Find the work done by magnetic field when the velocity of rod becomes ##v## and the heat energy liberated till that time.
Homework Equations
##V_{induced}=Blv##
##F=ilB##
The Attempt at a Solution
An emf is induced in the loop since flux due to ##B## increases. A retarding force ##F=ilB## acts.
$$i=\frac{Blv}{R}$$
$$F=\frac{B^2l^2v}{R}=-m\frac{dv}{dt}$$ (since velocity decreases as time increases)
Since the force due to magnetic field is the only force acting on the rod, its kinetic energy change is because of this force. But if there is current through a resistor, then there will be heat loss. But if all the work done is used for changing kinetic energy, where does heat come from?