Electromagnetic Induction Question

Hey,

Regarding induced currents as a result of a magnet falling through a conductor, I read in a textbook that 'the induced current will always produce a magnetic field which opposes the magnet's magnetic field'. Is this right?

My thinking is this:

At the top of the conductor, i.e. when the magnet (north-pole facing downwards) is just about to fall through, magnet's field lines are cut, so magnetic flux changes to emf is induced. Since magnetic flux has increased, the induced current will want to be in a direction such to decrease the magnetic flux and so would produce a north pole. Hence, the textbook holds here because the induced current's magnetic field would oppose the magnet's.

However, when the magnet is at the bottom of the conductor, magnetic flux decreases so hence the induced current will want to increase magnetic flux and so will induce a south pole to 'attract' the magnet's north pole. Hence, surely the induced current's magnetic field in this case is ATTRACTING the magnet's and not OPPOSING?

Thanks

@uberteknik really appreciate it if you could help me out man!

You are OK up to as far as the magnet leaving the solenoid.

This time it's the South Pole leaving that causes the change in flux. Which means the induced field will produce a North Pole attracting the South.

Have a look at these diagrams, pictures paint a thousand words.

http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/emfchb.html

Even still, wouldn't that be 'attracting' the magnet's magnetic field rather than opposing it?


Posted from TSR Mobile

Be careful with the definition of Lenz's law:

It's the change in flux which induces an e.m.f. and current in the solenoid which sets up a magnetic field to try and oppose the change in flux.

That means when the magnet enters the coil, the flux lines are increasing, the induced e.m.f. sets up a magnetic field to oppose that increase. i.e. it creates opposite poles to that entering the coil.

When the magnet falls through and out the other side, the flux lines start to decrease and the induced e.m.f. will set up a magnetic field to try and oppose that decrease.

In other words, the permanent magnet field direction has not changed, and in order to try and keep the magnetic field from collapsing, the induced e.m.f. sets up a magnetic field which tries to reinforce that of the magnets.

So yes, when the magnet drops into the coil the fields oppose. When the magnet drops out of the coil, the fields are aligned.

Thanks! So just so I'm sure - clearly the induced current will oppose the change in magnetic flux that causes it (Due to Lenz's Law), but this means that it will oppose the magnet's magnetic field when it enters the solenoid, and 'attract' or align with the magnet's magnetic field when leaving the solenoid? Hence the textbook's assertion that the induced current's magnetic field will always oppose the magnet's magnetic field is incorrect?

Thanks! So just so I'm sure - clearly the induced current will oppose the change in magnetic flux that causes it (Due to Lenz's Law), but this means that it will oppose the magnet's magnetic field when it enters the solenoid, and 'attract' or align with the magnet's magnetic field when leaving the solenoid? Hence the textbook's assertion that the induced current's magnetic field will always oppose the magnet's magnetic field is incorrect?

Yes. It should read will always oppose the change in the magnetic field.

You might find it easier to consider that the induced B field is always in the direction that makes the agent moving the magnet do work i.e. it makes the agent feel a force when pushing the magnet so that the agent loses energy, and the circuit gains it.

So when a N pole is moved into a solenoid, it sees a N pole at the nearest end. The agent moving the magnet is thus repelled, and expends energy moving the magnet closer to the solenoid.

When a N pole is moved out of a solenoid, it sees a S pole at the nearest end, and is therefore attracted towards the solenoid, and the agent expends energy moving the magnet away from the solenoid.

This ensures that energy is:

a) conserved - we don't get a perpetual motion machine
b) transferred from the motion of the magnet into electrical energy in the solenoid

You can then figure out the direction of the induced current/emf from the location of the N/S poles of the solenoid.

From this point of view, Lenz's law is a consequence of the conservation of energy - if the solenoid gains energy, then the agent moving the magnet loses energy.

Yes. It should read will always oppose the change in the magnetic field.