Energy changes during motional emf

[Abhishekdas]

Homework Statement

A U shaped conducting tube is placed in a constant magnetic field in the downward direction. On the left of the tube is a resistance R.All other rods are assumed resistance less.On this tube a conducting rod is moving with constant velocity towards right with the help of an external force...Now i was trying to figure out the energy chnges associated during the process...

Homework Equations

The Attempt at a Solution

Now we know that a motional emf is induced in the rod and a current is generated and due to this current a force is excerted on the magnetic field towards left. Now i wanted to figure out the energy changes in the process but i was not confident of what exactly was happening...Correct me wherever i am wrong...

Initially let's say the external force does work with power Fv and the magnetic field does equal amount if negative work...So net work on rod is 0.
Now coming to the emf part...The magnetic field creates the emf...Now normally when we talk about emf in a battery we say that chemical energy is converted to the energy required in doing the work required to push the charges arong the circuit...But in this emf where does the energy come from...?Is it the magnetic field which excerts forces on the electrons responsible for this energy?...And what about the energy which is dissipated by the resistance in the form of heat? Where does all these energies come from and what conversions take place? I am confused about that...So i would really appreciate some help on this...I want to develop my concepts on energy conversions in electricity and magnetism which i feel is much tougher that energy conversions in mechanics which seem much simpler...

PS: I have attached a digram to describe the basic setup...

 

[anathema]

Thank you for your question regarding the energy changes in a U-shaped conducting tube placed in a constant magnetic field and with an external force applied to a moving conducting rod. This is an interesting scenario and I would be happy to help clarify some of the concepts involved.

Firstly, you are correct in saying that a motional emf is induced in the rod as it moves through the magnetic field. This emf is created by the changing magnetic flux through the loop of the conducting tube. As the rod moves, the magnetic field lines passing through the loop also change, creating a changing magnetic flux. This changing flux induces an emf in the loop, which in turn causes a current to flow.

Now, let's address the question of where the energy comes from. In this scenario, the energy comes from the external force applied to the moving rod. This force is doing work on the rod, which is then converted into the energy required to push the charges around the circuit. As the rod moves, the external force is constantly doing work on it, maintaining its velocity and causing a current to flow.

In terms of energy dissipation, the resistance in the circuit plays a key role. As the current flows through the resistance, some of the energy is converted into heat, due to the collisions between the moving charges and the atoms in the resistance. This heat energy is then dissipated into the surroundings.

In summary, the energy changes in this scenario are a result of the external force doing work on the moving rod, which then creates a current and induces an emf. This current then flows through the resistance, dissipating some of the energy as heat. I hope this helps clarify the concepts involved. Please let me know if you have any further questions.