High School Magnetic Field Lab

[nmsurobert]

I attempted to run a lab that would allows us to calculate the magnetic field strength of a couple different neodymium magnets. I would love some feedback on it and ways that I could potentially make it better. The numbers I calculated were very far off from what I expected.

Apparatus set up:
I rolled up a three sheets of construction paper and made a narrow tube about a meter long. I made two of these. At the bottom of each one was a copper coil. Each one having different turns. The high number of turns was 60.

The experiment:
I dropped two different magnets through the tube and ultimately through the coil. Using a multimeter, I measured the voltage change as the magnet fell through the coil. I did this a few times and used an average reading of 11.5 mV. The set up with lesser turns averaged 3.5 mV.

The math:
I wanted to use Faradays Law to first determine flux. I knew N, and I knew emf, but I didnt know time. I used kinematic equations to determine velocity and then to determine the time the magnet was falling through the coil. I know those numbers were a little off. My calculated velocity was a little over 3 m/s, which seemed a little fast for me but I ran with it. Anyway, using that I found a time 't' that the magnet was falling through the coil and I was able to solve for flux.
I used flux = BA to solve for B. 'A' being the area of the coil. Ultimately my B-field was 10^-4 T. Which I am sure is way too small for the neodymium magnets I was using. I was expecting something like .1 T. I did the math a few different times and that was the smallest I could get the numbers.

Aside from any feedback, I have one question that I've been thinking about...
Was 60 turns enough? And with that question, does it matter how the coil is coiled? Would it have worked better is the coils where stacked on top of each other or more like a spring (which is how I set it up.)

Thanks!

 

[kuruman]

I have a couple of comments for starters.
1. Exactly how did you calculate the velocity of the falling magnet? Did you assume constant acceleration g down? If so, that is incorrect. The induced currents in the coil provide an acceleration up opposing the velocity. This is sometimes called "magnetic friction" or magnetic braking.

2. The expression flux = BA assumes that the magnetic field is constant over the area of the coil. That is not the case. The B-field of the magnetic depends on position. For a disk magnet is can be characterized by a dipole moment at distances much larger than the disk diameter, but unfortunately that is far from being the case here. In short, you need to be more specific about what you mean by the "strength" of a magnet. What is your definition of it?

 

[nmsurobert]

I have a couple of comments for starters.
1. Exactly how did you calculate the velocity of the falling magnet? Did you assume constant acceleration g down? If so, that is incorrect. The induced currents in the coil provide an acceleration up opposing the velocity. This is sometimes called "magnetic friction" or magnetic braking.

2. The expression flux = BA assumes that the magnetic field is constant over the area of the coil. That is not the case. The B-field of the magnetic depends on position. For a disk magnet is can be characterized by a dipole moment at distances much larger than the disk diameter, but unfortunately that is far from being the case here. In short, you need to be more specific about what you mean by the "strength" of a magnet. What is your definition of it?

1. I did use g as a constant. I know that opposing force exists, but I thought it could be negated. The magnet appears to be in freefall the whole way through the tube.

2. I know the orientation of the magnetic field coming from the magnet. The tube I dropped it through is too narrow for the magnet to be in any position but upright. Its essentially a bar magnet falling straight down. Either north end straight down or south end straight down. The magnet definitely doesn't have too much wiggle room as it makes it way down. By strength I mean determining B. Anytime I've purchased magnets they are usually labeled with "Field strength at surface". I know I'm not measuring at the surface, but I didn't expect the numbers to be so far off.

 

[kuruman]

Instead of me guessing, please show your step by step calculation of the B field at the surface and include relevant numerical parameters. For example, an object released from a height of "about a meter" would acquire a speed of 4.4 m/s. How did you get 3 m/s?

Also, the induced emf changes as a function of time both in magnitude and polarity as shown in the graph below. Is the 11.5 mV the averaged maximum of many tries?

The spread of the curve shows the time it takes the magnet to go through the coil but you need an oscilloscope to get that.

The field at some distance $z$ from the magnet, $B(z)$ varies as $1/z^3$. The plot below shows the ratio $\frac{B(z)}{B_0}$ plotted against distance measured in disk radii. Here $B_0$ is the maximum field at the surface. You can see that at distance equal to a disk diameter ($\frac{z}{R}=2$) the field is about 10% of the surface field. You may not expect the numbers to be far off, but they are.

 

[nmsurobert]

Instead of me guessing, please show your step by step calculation of the B field at the surface and include relevant numerical parameters. For example, an object released from a height of "about a meter" would acquire a speed of 4.4 m/s. How did you get 3 m/s?

Also, the induced emf changes as a function of time both in magnitude and polarity as shown in the graph below. Is the 11.5 mV the averaged maximum of many tries?
View attachment 279401
The spread of the curve shows the time it takes the magnet to go through the coil but you need an oscilloscope to get that.

The field at some distance $z$ from the magnet, $B(z)$ varies as $1/z^3$. The plot below shows the ratio $\frac{B(z)}{B_0}$ plotted against distance measured in disk radii. Here $B_0$ is the maximum field at the surface. You can see that at distance equal to a disk diameter ($\frac{z}{R}=2$) the field is about 10% of the surface field. You may not expect the numbers to be far off, but they are.

View attachment 279412

Your second paragraph really helps. I attempted to crunch some numbers considering the distance from the surface of the magnet to the coils but my numbers weren't too different.

I'm going to run it again tomorrow. I'll make sure to take more detailed notes as I run it and I'll reply to you after I've gone through it again. Thank you for replying. I have a heavy emphasis on labs in my class and lab set up, and I want this one to be as successful as my other labs.

 

[kuruman]

Good luck. Is this something that was assigned to you or something that you thought of on your own?

 

[nmsurobert]

Good luck. Is this something that was assigned to you or something that you thought of on your own?

I teach ap phys 2 at a high school. It's something I thought of on my own. I didn't get to run it last year because of the pandemic. I knew what I wanted to do, but I never to ran it. Students will run this lab next year if I can make sense of it.

 

[kuruman]

Sorry, I thought you were a student. I reported this post thinking it belongs elsewhere, but I guess it's fine where it is. Let me know what happens when you run it again and I might come up with some ideas in the meantime.

On edit: I now see that the mentors moved this thread to Classical Physics.

 

[nmsurobert]

Sorry, I thought you were a student. I reported this post thinking it belongs elsewhere, but I guess it's fine where it is. Let me know what happens when you run it again and I might come up with some ideas in the meantime.

On edit: I now see that the mentors moved this thread to Classical Physics.

Coming across problems like this makes me feel like a student lol.

I ran it again. I found some IR photogates which made getting the time much easier.
I dropped the magnet 20 twenty times and only used and found an average of 7mV. The smallest value the multimeter can read is 1mV. The coil I used had 80 turns. The photogate gave me a time of .0561s.

Solving for flux:
((7*10^-3)(.0561))/80 = 4.91*10^-6

Using flux to solve for B = flux/Area of the coil

(4.91*10^-4)/(1.53*10^-4) = .032 T

That number I am more happy with.

The area of the magnet is 5.03*10^-5. The difference in area between the magnet and the coil is 1.04*10^-4.

 

[kuruman]

The area of the magnet is 5.03*10^-5. The difference in area between the magnet and the coil is 1.04*10^-4.

The numbers are meaningless without units, nevertheless if the area difference is about twice the area of the magnet, this means that the area of the coil is 3 times that of the magnet. The picture below shows qualitatively a side view of the flux lines through the area (gray bar) of the coil. Setting the flux equal to BA, assumes that the lines are constant in magnitude and perpendicular to the area of the coil. This is not the case and overestimates the flux. It might be more realistic (although still not correct) to assume that the field is uniform over the area of the magnet and zero outside that area, in other words treat the disc magnet as a solenoid. This will boost the value of B by a factor of 3. It's not fudging but replacing something incorrect with something less incorrect.

 

[nmsurobert]

The numbers are meaningless without units, nevertheless if the area difference is about twice the area of the magnet, this means that the area of the coil is 3 times that of the magnet. The picture below shows qualitatively a side view of the flux lines through the area (gray bar) of the coil. Setting the flux equal to BA, assumes that the lines are constant in magnitude and perpendicular to the area of the coil. This is not the case and overestimates the flux. It might be more realistic (although still not correct) to assume that the field is uniform over the area of the magnet and zero outside that area, in other words treat the disc magnet as a solenoid. This will boost the value of B by a factor of 3. It's not fudging but replacing something incorrect with something less incorrect.

View attachment 279510

The units are meters. Sorry.
Do think this is a lab I should even run with the students? I had fun doing it. Setting up and trying to make sense conceptually of everything has taught me something. Of course I would cover problems with some of the assumptions that are made, like BA = flux or treating it as a solenoid.

 

[kuruman]

The units are meters. Sorry.
Do think this is a lab I should even run with the students? I had fun doing it. Setting up and trying to make sense conceptually of everything has taught me something. Of course I would cover problems with some of the assumptions that are made, like BA = flux or treating it as a solenoid.

I can only tell you what I would do if faced with this situation. I would ask myself, "what is the educational value of this experiment to the students in view of all the approximations and assumptions?" Personally, I would stop working on determining $B_0$ and consider something else that is related to it. I can think of two things

1. Investigate magnetic braking. Drop the magnet inside a vertical non-magnetic tube (I have use a 2-ft long aluminum tube of thickish walls ≈ 1 cm) and measure its speed as a function of position, or position as a function of time. Hall effect sensors along the length of the tube work well in this case or you might find a way to use your IR photogates. Students can determine the velocity vs time curve and see how fast the magnet reaches terminal velocity. Use the theoretical expression $v(t)=v_{ter}(1-e^{-bt})$ to determine the constant $b$. Add mass (e.g. stick iron washers but with a piece of plastic in between to make sure you can remove them) and see how the terminal velocity depends on the mass. If you have magnets of different strengths use the constant to rank them according to strength.

2. Investigate the power law of the magnetic force. Suspend the magnet above an iron plate and use a force gauge to measure the force of attraction as a function of height above the plate. Use spacers non-magnetic spacers to determine the separation between the magnet and the plate. Construct a semi-log plot to find the power law between force and separation. Use the y-intercept as a measure of the strength of the magnet. If you have magnets of different strengths use the y-intercept to rank them according to strength.

These are just suggestions. My own bias favors lab experiments that investigate the modeled functional dependence of a measured variable on a measured independent variable. Then, after one establishes the model through one experiment, one tweaks the model's parameters and verifies that it works (or not). That's how science works.

 

[nmsurobert]

I can only tell you what I would do if faced with this situation. I would ask myself, "what is the educational value of this experiment to the students in view of all the approximations and assumptions?" Personally, I would stop working on determining $B_0$ and consider something else that is related to it. I can think of two things

1. Investigate magnetic braking. Drop the magnet inside a vertical non-magnetic tube (I have use a 2-ft long aluminum tube of thickish walls ≈ 1 cm) and measure its speed as a function of position, or position as a function of time. Hall effect sensors along the length of the tube work well in this case or you might find a way to use your IR photogates. Students can determine the velocity vs time curve and see how fast the magnet reaches terminal velocity. Use the theoretical expression $v(t)=v_{ter}(1-e^{-bt})$ to determine the constant $b$. Add mass (e.g. stick iron washers but with a piece of plastic in between to make sure you can remove them) and see how the terminal velocity depends on the mass. If you have magnets of different strengths use the constant to rank them according to strength.

2. Investigate the power law of the magnetic force. Suspend the magnet above an iron plate and use a force gauge to measure the force of attraction as a function of height above the plate. Use spacers non-magnetic spacers to determine the separation between the magnet and the plate. Construct a semi-log plot to find the power law between force and separation. Use the y-intercept as a measure of the strength of the magnet. If you have magnets of different strengths use the y-intercept to rank them according to strength.

These are just suggestions. My own bias favors lab experiments that investigate the modeled functional dependence of a measured variable on a measured independent variable. Then, after one establishes the model through one experiment, one tweaks the model's parameters and verifies that it works (or not). That's how science works.

Ah those are both awesome ideas. Thanks again.