# Homework Help: Current induced in a loop of wire by a bar magnet (Conceptual)

1. Feb 22, 2012

### SMA777

1. The problem statement, all variables and given/known data

A very strong magnet is suspended by a non-magnetic thread. A student forms a loop out of a wire attached to the Pasco 750 Interface as shown on the left. During a half second interval, the student moves the wire loop until it is below the magnet as show

a) Describe (in enough detail) the resulting current versus time graph produced by the computer. If the current is non-zero at any time, could the current be the result of a magnet force on the positive charges in the wire? Explain.

Suppose that instead of the wire moving down, the magnet were pulled up. Assume that the magnet moves the same distance as the wire did, and in the same amount of time.

b) Describe (in enough detail) the resulting current versus time graph produced by the computer. If the current is non-zero at any time, could the current be the result of a magnet force on the positive charges in the wire? Explain.

2. Relevant equations

No equations; Conceptual

3. The attempt at a solution

for part (b) I've said:
As we saw in lab, it does not matter whether it is the magnet that moves, or the wire. It is the relative motion that induces the current. Thus, the current graph in this case, because the magnet moved the same distance as the wire in the same amount of time, and was pulled up (the wire was pulled down the magnet), the graph will be the same as in part a because their relative motion was the same.

Where I'm stumped is part a! I know that the magnetic field Inside the magnet points from south to north (so downwards), and I did the right hand rule assuming positive charge flows from red to black, and got the magnetic field induced in the wire to also be downwards. But I'm not sure what this means about the current graph of the wire (ie, when does it increase or decrease). I'm also not sure when/if it is ever 0?

Thanks for any help!

2. Feb 23, 2012

### PeterO

Ok Part A.

A south pole has magnetic field pointing into it while the North pole has magnetic field pointing out of it.
So in the first picture, that means downward B, above the magnet - and getting stronger the closer to are to the magnet [since it spreads more thinly as you move away fro the actual magnet] and downward field below the magnet - again getting weaker as you move away from the actual magnet.

As the coil is lowered over the S pole, the coil is subjected to increasing downward field, so will have an induced upward field [in a futile gesture to over come that increasing downward field.

One the magnet is enclosed in the loop, the field does not change, so no induced effects.

As the Coil drops away frm the magnet, it is subjected to a reducing downward field. it will thus have induce a downward field [in a futile attempt to make up for what is gradually disappearing].

So: first an an upward field, and then a downward field. [current from black to red] - the nothing - then a downward field [current red to black]

Note when the current flows from red to black, this makes the red terminal negative and the black terminal positive.
The coil is the driving component of a [potential] circuit - the battery if you like.
We are used to saying that current flows from the positive terminal of a battery to the negative terminal. But that is the current flow in the circuit . Think about which way the current is flowing inside the battery. [yes it is going the wrong way, but only because the chemicals are forcing it to do so: that's how batteries work]

3. Feb 23, 2012

### SMA777

Wow, thank you so much for your very, very helpful response PeterO! I really appreciate it.
Here is what I have gathered for Part A, based on that explanation

A. The magnetic field in the magnet points downwards (because the magnet inside has a magnetic field pointing north). When the coil is lowered around the magnet, it creates is own magnet field in order to "counter balance" this magnetic field. Thus, the coils magnetic field must point upward - i.e., a counterclockwise current. We see from the picture, that if this coil has a counterclockwise current, the current would be flowing from black to red, so a POSITIVE current. The current, as it approaches the top of the south poll of the magnet becomes stronger and stronger because the magnetic field it is trying to counter balance is becoming stronger. Then, the loop around the magnet shows no change in current because the magnetic field it is counterbalancing (that of the magnet itself), is not changing. Finally, when the magnet gets near the northern tip of the magnet, it DECREASES current to a negative current (clockwise flow, so from red to black) in order to create an upward magnetic field, to try to counter balance the magnetic field of the magnet which is now decreasing again in strength as you leave the magnet.

4. Feb 23, 2012

### PeterO

The description is not exactly as I would like.

It does not carry with it the idea that the current induced in the coil mirrors the rate of change of flux - the VARIATION in flux - it is subject to.

Also with the magnet itself. The field lines near the poles spread out, and thus the field becomes less intense as you move away from the pole. The field on the outside of the body of a magnet is firstly, very week, but more importantly pretty constant. If you were to move this coil through even a very strong, UNIFORM magnetic field you would get no induced current.

As the coil approaches the magnet, the last thing that happens is that the very strong field that exists at/just beyond the pole suddenly ceases to thread the loop - so you will get a short spike of current in the opposite direction to what you have had so far. When the loop finally passes the North pole of the magnet, there is again a sudden change from nothing to a massive field, so a brief spike in current is induced, then the field drops away again. So we have massive flux increase followed by gradual flux reduction. Indeed, as the coil approaches and departs from the magnet, the induced current can tend to be rather constant for a while, as the rate of change of flux can be fairly constant.

Your description reads like the coil is working to counteracting the magnet, rather than responding to the change in flux density / magnetic field changes it is subjected to.
It reads like the current will be getting stronger simply because the field itself is stronger, rather than because the rate at which the field strength is increasing is the important part.

That last idea I was trying to explain can best be shown if you consider just the first part - the coil approaching the magnet.
If the coil approaches slowly, the increase in flux is very gradual, so the induced current is very small - but it flows for quite a while, since a slow moving coil will take a long time to reach the magnet.
If the coil approaches rapidly, the increase in flux is very sudden, so the induced current is very large - but it flows for only a short while, since a fast moving coil will take only a short time to reach the magnet.
The net result is actually that the amount of charge that flows through the coil is approximately [exactly?] the same in each case.