# Lenz's law and conservation of energy

1. May 24, 2013

### annie122

I don't understand how lenz's law is a form of energy.
An explanation said if the induced current did not oppose change, we would be obtaining energy without doing any work.

I think my problem here is that I can't follow the

no change -> get free energy

logic.

2. May 25, 2013

### tiny-tim

hi annie122!
no, it means that if the induced current "supports" the change in magnetic flux, we'd get free energy … both the current and the flux would be increasing in energy!

(and if there's no induced current, there's no problem)

eg if you have two circular wires, with a current in one inducing a current in the other, then the second current will tend to reduce the first current rather than increase it …

the energy in the second circuit is being drained from the first circuit!

3. May 25, 2013

### annie122

Thanks. :)

I got this part.
But I realized I've been missing something really important.

I'm going to ask a really fundamental question;so current and flux are forms of energy?

In currents, electrons are moving, so more current -> more KE in energy?

How is flux related to energy?

4. May 25, 2013

### rude man

Take a permanent magnet bar and move it towards a coil, inducing a current in the coil. Say you move the N pole towards the coil.

If the current induced went the other way you would have made a magnet out of the coil with its S pole facing the bar's N pole, attracting the bar to the coil. You would have generated heat in your coil - free energy! That violates the conservation of energy. Plus, the coil's B field (and flux) was built up, again with no energy input.

In reality, your coil would actually have generated a N pole facing the bar magnet, repelling the bar from the coil. If you still want to move the bar towards the coil you would have to push the bar towards the coil. This time you generated the energy necessary to heat up the coil and build up its magnetic field.

Building up a magnetic field takes energy. It can be shown that the energy density (joules per unit volume) of a B field = B2/2μ.

5. May 25, 2013

### annie122

Okay, that got me cleared up on that, thanks.

Is this because since there's always resistance in the coil, inducing current produces heat by the I^2R law?

6. May 25, 2013

### rude man

Right.

If the coil were a true superconductor with zero resistance then you could not move the bar towards the coil at all! I believe somebody is hoping to develp superconductor rails for levitating trains which would work along the same idea.

7. May 25, 2013

### annie122

Can you explain this part?
So to summarize:
If current went in the same way,
1) the B-field, which requires energy to make stronger, would be strengthened, and
2) the coil would give off more heat without me doing any work (or rather would it be negative work, since the field is in the direction of motion?)
Therefore the current must be in the opposite direction.

8. May 25, 2013

### rude man

If the were no resistance then if you could move your magnet bar you would be generating a finite emf and infinite current = emf/0, creating an infinitely strong magnet from your coil, so you couldn't move the bar!

I'd say yes for 1) and 2). Don't know about 'negative work' but I suppose yes, the work would be negative if the bar were sucked into the coil instead of havig to push it in.

To make your life more complex: a permanent magnet will attract iron pieces, which means work is done by the magnet since the pieces had to be accelerated, which means force, and force times distance = energy (work). So where didthat energy come from? What happened to energy conservation?

The answer is that the "amperian currents" surrounding a permanent magnet, making a sort of electromagnet like a solenoid, see no resistance and so do not dissipate energy. This gets into quantum mechanics with which I have as little to do as possible!

9. May 25, 2013

### anhnha

Impressive!
Can you explain why the work is negative?
I am still not clear with this answer. Can you give it more detail or a link explaining about that?

10. May 25, 2013

### rude man

If the coil had sucked the bar into the coil the work would be negative because F would be opposite in direction to displacement - I mean the force you would have to "exert" to move the bar. Instead of you exerting force on the bar, the bar wouild be exerting force on you!

Or how about this: you take a relxed spring and pull it a distance x. You have exerted work = integral F dx = kx^2/2 and that energy is stored in the spring.

You then allow the spring to get back to its relaxed position, but still holding on. Now you have "exerted" negative work on the spring and the spring stored energy = 0. The spring's stored energy went to pulling your hand thru the distance x. You have performed negative work on the spring.

Last edited: May 25, 2013
11. May 26, 2013

### anhnha

Thanks, I have problem in understanding negative work.
Yes, in this case I understand. I have to exert a force onto the spring.
This part is confusing me. In this situation, I do nothing. There is a force of spring exert on my hand and the work of spring is positive work.
But I do nothing and I don't exert a force onto spring then how can the negative work possible?

12. May 26, 2013

### milesyoung

I think that's stretching it a bit. It's akin to asking where the energy comes from for gravity to accelerate mass.

The system of the permanent magnet and iron pieces will have potential energy by virtue of its configuration of magnetic moments. The principle of energy conservation still holds.

13. May 26, 2013

### rude man

Good point. What I wanted to do was to distinguish between the magnetic field generated by the coil, which requires work to set it up, and the existence of the permanent magnet's field which does not.

Thanks.

14. May 26, 2013

### rude man

You don't 'do nothing'. You resist the force pulling the spring back to its rest state. So the force you apply is opposite to the displacement and work = force (vector) doted into displacement (vector) which here is clearly negative.

15. May 26, 2013

### anhnha

The force that I exert to the spring and the force of spring pulling back are equal?
If so how can the spring move back to the rest state because it starts at rest when spring are pulled to the maximum position?

16. May 26, 2013

### rude man

I don't understand the question.

1. You pull the spring from rest position to position x. You perform positive work in doing so. You hold the spring at position x.

2. You allow the spring to go back to its rest position while still holding onto the spring. You have to resist the spring pulling itself back. The force you apply in going from x to zero is negative and so the work you perform is negative.
.

17. May 26, 2013

### anhnha

Let's me express my quesion more detail.
In this case the force that I exert to spring is in the opposite direction of spring's moving.
There are two force exert to spring.
The pulling force from x to 0 and the force that I exert with the opposite direction.
Do the two forces have the same magnitude but oppsite directions?
If so(two forces equals in manginute) then how can the spring move to the rest state?

18. May 26, 2013

### rude man

good question.

As you allow the spring to return to its rest position you are gradually reducing your restraining force. In fact, the restraining force at any point x is kx as you go along from x to zero.

If you do this infinitely slowly then the two forces are always equal and opposite. If you do it faster then you'll have to ask an ME what goes on ... there will be accelerations and decelerations which implies unequal forces but I'm not sure what the equivalent mass would be - your hand or ???.
.

19. May 26, 2013

### anhnha

Thanks, got it
What is "ME"?

20. May 26, 2013

### milesyoung

For simplicity's sake, let's assume the spring itself is massless and it's the displacement of a mass attached to its movable endpoint we're considering. If the force exerted by the spring and your hand on the mass are equal in magnitude and opposite in direction, and there are no other forces applied to it, there is no net force on the mass and it won't accelerate.

I think your confusion comes from the fact that you're applying Newton's third law incorrectly. Consider the mass alone:
- The spring exerts a force on the mass and the mass thus exerts a force equal in magnitude and opposite in direction on the spring.
- Your hand exerts a force on the mass and the mass thus exerts a force equal in magnitude and opposite in direction on your hand.

This is true whether or not the force exerted by the spring and your hand on the mass are equal in magnitude.