In the above question find the force required to move the rod with constant velocity `v`, and also find the power delivered by the external agent.

Explanation

The force needed to keep the velocity constant
`F_(ext)=ilB=(B^(2)l^(2)v)/(R+r)`
Power due to external force `=(B^(2)l^(2)v^(2))/(R+r)=epsilon^(2)/(R+r)=i^(2)(R+r)`
Note that the power delivered by the external agent is converted into joule heating in the circuit.That means magnetic field helps in converting the mechanical energy into joule heating.