# Lenz's Law and conservation of energy.

## Main Question or Discussion Point

Hello everyone, first time posting in here.
Heres a question, in Lenz's Law, it states that the current produced will be opposite of the motion that created it. This is done by the repulsion or attraction force created by the solenoid to counter the motion of the magnet. Now, without the work done created by the solenoid's counter poles to the magnet's motion and it overcoming it, there can be no current due to the conservation of energy. But without a current how does the solenoid form an electromagnet with the poles to counter the magnet's motion.

Hence which one came first, the current that produces the electromagnet, or the poles of the electromagnet that causes work done thereby creating current.

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Well, a solenoid w/o current has no H field. A current is accompanied by an H field. As the current changes from zero to non-zero, the magnetic flux, phi, changes as well. An emf accompanies the original current, and the time changing flux includes a counter emf, which acts in an opposite direction to the original, per Lenz' law. Make sense?

Claude

well i mean induced current, how does it form? I know change in magnetic flux, but how would the current come out of nowhere. Meaning, shouldnt the solenoid or coil of wire have to have poles first?

Dale
Mentor
Meaning, shouldnt the solenoid or coil of wire have to have poles first?
No, that is not necessary. In fact, some magnetic fields do not have what could be described as "poles" anyway. An example is the magnetic field around a long straight wire which goes around in a loop without ever "concentrating" into a dipole field.

Lenz's law only requires that the induced current oppose the change in magnetic flux, not that the field have poles.

ok but how does the conservation of energy apply? Where does the current come from? I know from movement but how is that energy converted into electrical energy

Dale
Mentor
It is important to understand that the fields themselves have energy. Roughly speaking, by generating a field which opposes the field you are reducing the energy stored in the field. This energy is then available to the current to do work.

but how do u generate the field that opposes the field?

but how is the current generated without the magnetic field ?  Hence which one came first, the current that produces the electromagnet, or the poles of the electromagnet that causes work done thereby creating current.
Neither, they grow together.

If you switch on/off a supply to a pure conductor or resistor the current increases/decreases almost instantaneously to its maximum value.

If you do this to a component with inductance the current takes measurable time to reach its final value.

Your components have inductance and exhibit this behaviour.

The physics behind Lenz law is the reason that current in an inductor cannot change instanteously. Faradays law, which incorporates Lenz law, provides a mathematical statement for calculation purposes.

Have you come across inductance and Faraday's law yet?

Dale
Mentor
but how is the current generated without the magnetic field ?  By the induced E-field
$$\nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}} {\partial t}$$
and by Ohm's law
$$\mathbf{E} = \frac{1}{\sigma} \mathbf{J}$$

Dale
Mentor
JadenErius, looking at Studiot's response I realize that I may have been answering the wrong question. Is your question one of timing of the various elements of electromagnetics? If so, the answer is clear: they all happen at the same time.

Just like in Newton's 2nd law, F=ma, the force does not happen first and then the acceleration, but rather they are always found together. If you were to find a situation where there was a force coming first without an acceleration yet then the law would be violated. Similarly with Maxwell's equations.

Hmmm makes sense and I have encountered faraday's law but not inductance though. But if my understanding of what your saying is that the current, the formation of the poles and the magnetizing of the coil of wire happens at the same time?
An explanation in inductance would be good though

Dale
Mentor
But if my understanding of what your saying is that the current, the formation of the poles and the magnetizing of the coil of wire happens at the same time?
Yes. All of that happens at the same time that the flux changes in the loop.

What is inductance then, does it affect this topic?

bump hello?

Dale
Mentor
What is inductance then, does it affect this topic?
As far as what inductance is, here is the Wikipedia page on inductance:
http://en.wikipedia.org/wiki/Inductance

Inductors store energy in a magnetic field, and the sign of the voltage across an inductor is determined by Lenz's law, so yes they are related.

interesting, i think i get it to a certain level. Thanks a bunch guys