The nail attached to the batteries

It's not.

 

....my partner and I disagreed with its structure.

That's very restrained of you. It is such a poor description of what to do it deserves more robust judgement.

 

"First you have to wrap the wire around the nail and leave a little off to be able to connect to the batteries. Make loops at both ends of the wire on the nail. Then arrange the batteries where the negative end of one battery is close to the positive end of the other battery. Have the copper wire touch the positive (+) of one battery and the negative (-) of the other battery. The end of the copper wire exposed must touch the positive (+) of one end of the battery and the negative (-) of the other battery. Use the nail to pick up paper clips. The nail attached to the batteries and wire will act as an electromagnet. The nail will pick up metal items because of the creation of magnetic force."

Loops? hmmm... The nice thing about 9V batteries in series is that one batteries negative will snap onto the other batteries positive. The wire cutter is never mentioned as ALL of the wire will be wound around the bolt unless that is a huge spool of wire. IF the batteries had to be wired parallel then 2 short pieces of wire would need to be cut to make the connections between the batteries. I will also add that "21G" wire is easily broken by hand by repeated bending without the need of cutters which while not necessary are a convenience.

 

I'm a teacher and my students were presented with this as a constructed response on a district test.
(A question they need to answer). I'm exasperated b/c I feel like this is way above their level of knowledge and understanding. We studied basic electromagnets and made one in class already with a D Battery or AA or 1 9V. But they were never taught about putting 2 batteries together so I didn't think it was a fair question for them to have to answer but they tried their best.

THE QUESTION:
Given the following supplies:

• 2 9V Batteries,
• 21G Copper wire,
• an iron Bolt
• wire cutters
  How would you set this up as an ELECTROMAGNET giving it the ability to pick up the most paperclips?

Background Knowledge:
In class they had only ever made a regular electromagnet using a D battery or a AA battery.
How would you put it together. ???

Hello, and welcome to the forum.

This is a rather strange question for what I gather are elementary school kids? Maybe high school kids would be a bit better.
I say this because this falls under the general category of an optimization problem because of the word "most", and optimization problems are usually more advanced and could require calculus as well as a decent understanding of the physics involved.

As to figuring this out in a simpler way here is how you might start...

First, the force is the main issue when it comes to attracting objects with an electromagnet, so you want to maximize the force, usually called the strength of the magnet. The force goes up with the more current through the wire, and goes up with the number of turns. Unfortunately, the resistance also goes up with the number of turns, and we don't really know how much wire we have to work with so we don't know if we can parallel two or more strands to allow a higher current through the wire(s). We could assume just one strand though I guess. That would handle about 1 amp without too much trouble, so I guess we have that fixed at 1 amp and no more unless the magnet is to be run for a short time only.
The force also goes up with the area, but the area would be fixed at whatever size the bolt head is.
Since we have that 1 amp fixed (for now) we want to wind as many turns as we can on the bolt as that will maximize the force. If the length of wire is limited, that means wind the entire length on the bolt. You can do it in layers. There is a limit, and in this case the limit would be that which allows the batteries to actually pump 1 amp through the wire. As the wire gets longer, the resistance increases, and so with a given battery voltage the current will decrease. However, if there is not enough wire then the wire will overheat. Probably the best compromise is to look up the resistance of #22 AWG copper wire, then figure out the length that would cause a current of 1 amp to flow in the wire and use that length.
This also places a constraint for how to connect the two batteries. Since we want 1 amp and we want as much wire as possible, we would want to connect the two batteries in series (again assuming only one strand of wire). That gives us a nominal 18 volts, and since i=V/R, and we can set R with the length of wire, we simply have to solve 1=18/R for R, and that is easy to do.
The best shape would be that which places more turns toward the front of the magnet, but since we have a, presumably iron/steel bolt, most of the flux will be concentrated in the bolt.
The leakage inductance will increase for turns farther out from the bolt, so we probably want to wind the layers over the whole length of the bolt body. This puts the most turns as close to metal as possible.

Since this problem is so advanced though, there is always the chance that the instructor (or whoever invented the problem) had a limited view of what goes into making one of these things, and thus they may base the result on what limited knowledge they have on hand.

Just to note, steel bolts do have much higher permeability than air, but much less than a magnetic material made for magnetic applications has. That means a steel bolt is not the best choice for a core either. If we were to use those laminations used for line frequency transformers for example, we would get a much better electromagnet out of it.

As a final note, if we could bend the bolt around into a "U" shape, we would get more strength out of it. The problem with a single straight bolt is also that there is a lot of leakage flux because one of the paths from one end to the other is through the air. That means we lose strength there too unfortunately.

I think I've covered this in enough detail but others may want to add to it also.

 

Hello, and welcome to the forum.

This is a rather strange question for what I gather are elementary school kids? Maybe high school kids would be a bit better.
I say this because this falls under the general category of an optimization problem because of the word "most", and optimization problems are usually more advanced and could require calculus as well as a decent understanding of the physics involved.

As to figuring this out in a simpler way here is how you might start...

First, the force is the main issue when it comes to attracting objects with an electromagnet, so you want to maximize the force, usually called the strength of the magnet. The force goes up with the more current through the wire, and goes up with the number of turns. Unfortunately, the resistance also goes up with the number of turns, and we don't really know how much wire we have to work with so we don't know if we can parallel two or more strands to allow a higher current through the wire(s). We could assume just one strand though I guess. That would handle about 1 amp without too much trouble, so I guess we have that fixed at 1 amp and no more unless the magnet is to be run for a short time only.
The force also goes up with the area, but the area would be fixed at whatever size the bolt head is.
Since we have that 1 amp fixed (for now) we want to wind as many turns as we can on the bolt as that will maximize the force. If the length of wire is limited, that means wind the entire length on the bolt. You can do it in layers. There is a limit, and in this case the limit would be that which allows the batteries to actually pump 1 amp through the wire. As the wire gets longer, the resistance increases, and so with a given battery voltage the current will decrease. However, if there is not enough wire then the wire will overheat. Probably the best compromise is to look up the resistance of #22 AWG copper wire, then figure out the length that would cause a current of 1 amp to flow in the wire and use that length.
This also places a constraint for how to connect the two batteries. Since we want 1 amp and we want as much wire as possible, we would want to connect the two batteries in series (again assuming only one strand of wire). That gives us a nominal 18 volts, and since i=V/R, and we can set R with the length of wire, we simply have to solve 1=18/R for R, and that is easy to do.
The best shape would be that which places more turns toward the front of the magnet, but since we have a, presumably iron/steel bolt, most of the flux will be concentrated in the bolt.
The leakage inductance will increase for turns farther out from the bolt, so we probably want to wind the layers over the whole length of the bolt body. This puts the most turns as close to metal as possible.

Since this problem is so advanced though, there is always the chance that the instructor (or whoever invented the problem) had a limited view of what goes into making one of these things, and thus they may base the result on what limited knowledge they have on hand.

Just to note, steel bolts do have much higher permeability than air, but much less than a magnetic material made for magnetic applications has. That means a steel bolt is not the best choice for a core either. If we were to use those laminations used for line frequency transformers for example, we would get a much better electromagnet out of it.

As a final note, if we could bend the bolt around into a "U" shape, we would get more strength out of it. The problem with a single straight bolt is also that there is a lot of leakage flux because one of the paths from one end to the other is through the air. That means we lose strength there too unfortunately.

I think I've covered this in enough detail but others may want to add to it also.

Before middle school I was in class learning about magnets. So, your underestimating just how bright the little ones are.

 

Hello, and welcome to the forum.

This is a rather strange question for what I gather are elementary school kids? Maybe high school kids would be a bit better.
I say this because this falls under the general category of an optimization problem because of the word "most", and optimization problems are usually more advanced and could require calculus as well as a decent understanding of the physics involved.

You are WAY overthinking it. The way that a sixth grader does -- and is expected to -- interpret the word "most" is not the same way that a graduate engineering student would be expected to interpret it.

 

You are WAY overthinking it. The way that a sixth grader does -- and is expected to -- interpret the word "most" is not the same way that a graduate engineering student would be expected to interpret it.

Well that's the way I see it, you certainly are not being forced to agree. She did ask "how you would do this", so I told her.
So you are saying a sixth grader sees this as an advanced optimization problem? That's interesting.
I guess you would just wrap turns around it and hope for the best then?

 

Before middle school I was in class learning about magnets. So, your underestimating just how bright the little ones are.

Some of the high school kids are pretty smart, not sure about the elementary school kids these days.

 

Well that's the way I see it, you certainly are not being forced to agree. She did ask "how you would do this", so I told her.
So you are saying a sixth grader sees this as an advanced optimization problem? That's interesting.
I guess you would just wrap turns around it and hope for the best then?

No, YOU are the one saying that because the question used the word "must" that a sixth grader is expected to see this as an advanced optimization problem involving a deep understanding of physics and calculus. I'm saying that that is NOT how a sixth grader interprets words like "most" and "best".

 

No, YOU are the one saying that because the question used the word "must" that a sixth grader is expected to see this as an advanced optimization problem involving a deep understanding of physics and calculus. I'm saying that that is NOT how a sixth grader interprets words like "most" and "best".

Oh ok, ha, that makes more sense now. Oh the word was "most" which is a superlative which begs for an optimization that's why I pointed that word out.

I wasn't really targeting sixth graders per se, just thought it might be that.
High schoolers may have already had some calculus.

I did offer a simpler way to go about it too.