Physics lab formula question - help please

[lloyd21]

Homework Statement

An ideal solenoid is expected to generate a dipole field that falls off quickly as you move away from the solenoid. The magnetic field at distance r along the axis of the solenoid is given by B = (Mo/ 2pie) (M/r^3) In this equation the parameter M is called the dipole moment and it is equal to M = NIA where N is the number of turns, and A
the cross-sectional area of the solenoid.
Calculate the value of the M , knowing that the number of turns in the solenoid you have is 1080 and the corss-sectional diameter is about 7.5 mm. Enter your measurements from the table above into the Logger Pro program and plot B vs r for each side of the solenoid. Then, perform a “variable power” fit of the form Y=AX^n with n set to -3 and identify the value of of the fit parameter A
Using the data you now have determine the value of the permeability of free space MoBe careful with the units

Homework Equations

The Attempt at a Solution

I have;

B= -.020mT = -.000020 T

2(p) = 6.28

M= 1.43x10^-3 Am^2

r = 20mm = 0.020m

fit parameter A = 0.7090

WHERE does the new A be placed ^?

 

[marcusl]

From your equations for B and Y, you can see that A_fit = M_0 * M / (2*pi). You are supposed to find a value for M0.

 

[andrevdh]

It seems that the instructions are telling you to set the gradient of the power fit graph to the suggested value for A in Logger Pro.

 

[lloyd21]

Yes I understand that, which I did. I found the Value for A with the new equation Y=Ax^-3 ...I just don't understand why I need that A when they gave me an A already for the formula..

 

[andrevdh]

Maybe they first want you to verify the power -3 with the supplied A
and then fit again with the power to obtain an experimental value for A?

 

[lloyd21]

Maybe they first want you to verify the power -3 with the supplied A
and then fit again with the power to obtain an experimental value for A?

the supplied A comes from the radius of 7.5mm ...solve for that A and you can solve M=NIA ...therefor I have B,r, and M and should be able to solve for Mo without anything else...I just don't get why they say with this new "data" you can now solve - which I thought I could have before without the new A

 

[andrevdh]

This is getting confusing, especially since there are talk of two As!
I get the cross sectional area of the solenoid as 4.42x10^-05 m².
I tend to agree with marcusl that you are suppose to use the obtained A form the power fit to calculate mu_zero - the permeability of free space.
This value of A from the power fit might be what they are referring to as the "new data".

 

[lloyd21]

I got the same cross sectional, i tried using the new A from the graph to solve for M and then solve for Mu_zero, however the answer is 7.4x10^-5, which is no where close to the actual value for Mo

 

[andrevdh]

I don't think you are suppose to "solve" for the magnetic dipole moment. You should calculate its value from the experimental values and then solve for mu_o using the fitted value of A.

 

[lloyd21]

Yeah I got that, by solve for M i meant find M (calculate M with the new A) and then solve for Mo...with the new formula...which gives that outrageous number still...

 

[andrevdh]

M = amount of turns x current in coil x cross sectional area

 

[lloyd21]

yes...which I show in the work above...so are they saying put my "new value" A( .7090) in for my cross sectional^

 

[andrevdh]

was the current about 30 mA?

 

[lloyd21]

yeah 0.03 on the dot

 

[andrevdh]

did you get the A (= 0.7090) fit parameter from logger pro by inserting n = -3?

 

[lloyd21]

yes

 

[andrevdh]

I assume you have a set of measurements where you measured the magnetic field at various distances from the central axis?
Could you maybe attach it here?
Another thing that is worrying me is that one gets two different probes. One for measuring the axial and another for the radial component of the magnetic field.
I am trying to find your formula in some literature, but have not been successful yet.

 

[lloyd21]

did you get the A (= 0.7090) fit parameter from logger pro by inserting n = -3?

That's why when I put in 0.7090, the results seem to be way off

 

[lloyd21]

I assume you have a set of measurements where you measured the magnetic field at various distances from the central axis?
Could you maybe attach it here?
Another thing that is worrying me is that one gets two different probes. One for measuring the axial and another for the radial component of the magnetic field.
I am trying to find your formula in some literature, but have not been successful yet.

B (T)

r(mm)B(T)

r(mm)

-0.02

200.02

20

-0.019

210.019

21

-0.018

220.018

22

-0.017

230.017

23

-0.016

240.015

24

-0.015

250.014

25

-0.013

260.013

26

-0.011

270.012

27

-0.008

280.01

28

-0.007

290.009

29

 

[lloyd21]

those are kind've hard to read, but the magnetic field is about -.020mT

 

[andrevdh]

I'll analyze it. Going to take a while, but I will most likely get what you got for A.

 

[lloyd21]

After the value of A is found is where I get stuck completely...

 

[andrevdh]

That might be that the experiment was not carried out correctly or the instrument was not used correctly ...

 

[lloyd21]

Thats why I posted on here, hoping that wasnt the case haha!

 

[andrevdh]

I did not force it throught the origin. My fit gives A = 1.306 x 10^-7 Tm³
which gives a value of 5.76 x 10-4 H/m for mu_o. Sorry that is how far I can help you.

 

[lloyd21]

thank you though for your response and help!

 

[andrevdh]

It seems that your data is way off. The magnetic field should have been the B* values according to the given formula

 

[lloyd21]

Isn't the magnetic field just the recording of the magnetic sensor as i move it away in 1mm increments from the solenoid?

 

[andrevdh]

Just make sure that my calculated values for B* is correct. One would think so yes, but there is quite a difference between the measured and the expected values - B*, so something is seriously wrong with the experiment, the apparatus, the procedure or ...? Plus the datapoints do not really conform to a straight line graph.

 

[andrevdh]

I only notice it now, but you were suppose to measure the field outside one end of the solenoid as you move further and further away. Since the coil is so small I assume that is what you did? The question then arises how one is suppose the measure r, form the end or ...? The formula suggests that at r = 0 one gets an unrealistically large magnetic field? Do you know what the length of the solenoid is?

 

[lloyd21]

I only notice it now, but you were suppose to measure the field outside one end of the solenoid as you move further and further away. Since the coil is so small I assume that is what you did? The question then arises how one is suppose the measure r, form the end or ...? The formula suggests that at r = 0 one gets an unrealistically large magnetic field? Do you know what the length of the solenoid is?

Sorry for the late response, the solenoid is very small, approximately 2cm

 

[lloyd21]

Sorry for the late response, the solenoid is very small, approximately 2cm

 

[andrevdh]

This is another indicator that the measurements could not be correct.
If you calculate the magnetic field inside of the solenoid with the standard formula
B = mu_o IN/L one gets 0.002 T.
Your measurements outside of the solenoid are larger than this value.
Did the magnet have an iron core? This could explain the larger measurements.

 

[lloyd21]

How did you get the numbers for B*(T) ... I just re did the lab again and got different numbers. this is my graph with the fit...https://attachment.outlook.office.net/owa/ChadNiddery@hotmail.com/service.svc/s/GetFileAttachment?id=AQMkADAwATYwMAItYTJhMy05YjY4LTAwAi0wMAoARgAAA1%2BGrg4JVahNrFK%2BtBRQxHMHABLpo8Xq25xEnBcsyMWzy8YAAAIBDAAAABLpo8Xq25xEnBcsyMWzy8YAAABJcj45AAAAARIAEADCm1IHbFWERrKKATpfIEQP&isImagePreview=True&X-OWA-CANARY=MExmzr-Mc0SI8-cmfdNr6lBhb1Ua_9IYsqRCrXT1KBke2gOlwMc_Hyqk1XEIOO0im2agejgNszg.&token=ab71b942-38cf-4b84-98f8-6722154f1278

 

[lloyd21]

the magnetic field recorded i converted to Tesla from mT, and converted the mm, to m

 

[lloyd21]

My professor said this as well..What you want to do is to compare your fit (Y = Ax^n, with n=-3) to the theoretical relation (B = (u0/2pi)(M/r^3) ) . Comparing the two formulae can tell you what the fitted parameter "A" represents.

 

[andrevdh]

I calculated B* from the given formula - the 1/r³ one.

Yes, so the fitted A parameter should give you the experimental value for u_oM/2pi.

Was the core of the solenoid "empty" (filled with air), or did it have some material in it?

 

[lloyd21]

It doesn't say if it was filled or empty...I'm so frustrated

 

[andrevdh]

Did you see something inside of the core (middle) of the solenoid?
Do not worry it will not influence the processing of your data.
I am just trying to make sense of the results.

 

[lloyd21]

No nothing?...

 

[andrevdh]

So there was "air" inside of the core?
That would mean that u_o is applicable here.

 

[lloyd21]

I don't follow? I'm not understanding what my next step is...

 

[andrevdh]

See my #37 post.
That means you can calculate u_o from the fitted A parameter's value.

 

[lloyd21]

Andre, I think I might have it now. But I need a little more help . This is what I am told. and here are my two new graphs.

You need two separate graphs...one for each side.
With your plot you want to determine u0. What you are doing is assuming u0 is unknown, and then using the data to determine u0. Of course, in reality, the value for u0 is known. Hence, by comparing "your" value for u0 to the known value gives an idea how well your experiment went.
To determine u0 you have B = (u0/2pi)(M/r^3), or rewritten: B = (u0 M/2pi)r^(-3). Another way of writing this would be Y = Ax^(-3), with Y and x being variables. If were to write B = (u0 M/2pi)r^(-3) as Y = Ax^(-3), what value would you ascribe to "A".

I think those look right. Now in your post 37# to find B, I get 12500 which seems off for the magnetic field. So how do I get B now to solve for the experimental Mu? And do I do that with both graphs to get two different experimental values for Mu?