# Source of torque on a frictionless DC generator

The image below shows a Faraday Disk DC generator. Let's assume that the bearings on the spinning metal disk are frictionless and that we give it a good spin and let go of the handle. I know from the conservation of energy that if the device is allowed to discharge through a load that it will eventually come to a stop. However, it is not obvious to me how a torque is generated in the disk through the action of the electrons dumping their energy out through the load (i.e. light bulb). Thanks in advance for clarification on this. • I've never seen one of these generators in operation but I would expect even without a load it would stop fairly quickly just from eddy currents. – M. Enns Feb 26 '17 at 19:43
• @M.Enns It is called a homopolar generator. en.wikipedia.org/wiki/Homopolar_generator – Farcher Feb 26 '17 at 20:13

The induced emf produces an induced current in such a direction as to oppose the motion producing it -Lenz's law.

In the diagram the direction of the conventional induced current is from the central spindle to the rim.
This is the direction of force $F$ in your diagram.

The disc carrying an induced current in that direction feels an upward force which is in the direction opposite to the direction of motion of the disc.
There is the source of the torque in opposition to the motion of the disc.

• So, is there no real connection to the load in generating the stopping torque? What if instead of attaching a load we had a superconducting circuit with R ~ 0? I guess what I'm hanging up on is the conservation of energy. Where is the energy of the rotating disc being transferred to? – Qubit1028 Feb 26 '17 at 20:54
• If the induced current is larger the opposing force (torque) is larger so the disc slows down faster. So the delivery of a higher electrical power by the generator produces a larger rate of decrease of kinetic energy. The kinetic energy of the disc is converted into electrical energy which in turn produces heat in a resistor if that is the load. – Farcher Feb 26 '17 at 20:58
• If I disconnect the disc from the load completely and allow it to spin freely on its frictionless bearings wouldn't the same Lenz's force be operational since the electrons passing through the magnetic field will still feel a force pushing them towards the rim? If so, wouldn't that imply that the disc would stop spinning even though there is nowhere for its kinetic energy to be transferred to? – Qubit1028 Feb 26 '17 at 21:14
• Eddy currents generated in the copper disc. – Farcher Feb 26 '17 at 21:17

When electrical power is being taken from the generator, a current must be flowing. That current makes the generator act like a motor, but with the motor torque opposing the rotation. That torque times the rotation speed is power, which in a perfect generator is the same electrical power being delivered.

When the circuit is disconnected, no current can flow, and no backwards torque is developed in the generator. Of course since power is current times voltage, no electrical power is being delivered by the generator either.

• Whoever downvoted this, I'd like to understand what is wrong. – Olin Lathrop Feb 27 '17 at 12:56
• I like your explanation. So, this is the counter-emf you are referring to, correct? If there are no friction losses in this generator, then all of the torque I put into the disk by hand just matches the backwards torque that the motor is applying to my hand. Is that the correct reasoning? – Qubit1028 Feb 27 '17 at 22:49
• @Quib: Yes. --- – Olin Lathrop Feb 28 '17 at 13:11