Calculating Permeability of Free Space with Ampere's Law: B-Field Lab Help

[cukitas2001]

Hello all,
Im trying to do this magnetic field lab and am having trouble with the very last question. It goes: "Assuming the equation (Ampere's Law: B=unI) applies for the solenoid, calculate the value and uncertainty of u (permeability of free space) using the graph of B vs. n.

In this part of the experiment we had a constant current through a slinky and measured the magnetic field as we changed the number of turns of the slinky.

I made my graph os B vs. n and it has a exponential looking relationship so i chose that as my trendline in Excel. Is this correct of should it have been a Power trendline? I chose exponential since it fits the data better.

The equation of my exponential trendline was y=18.473e^(15.161x)

so n is y and x is b and the rest of the garbage there is u and I. If i could only isolate the u and I...what i tried was multiplying both side by ln but i got stuck becasue i don't remember my log rules :-(. What i have right now is ln(n)=15.161x*2.91631. Am i on the right track? i also have the table of values and graph of this if it would help any.

 

[Saketh]

Look at the provided equation ($$B = \mu n I$$) and look at your data. Does an exponential curve make sense? (Hint: Find the theoretical slope of a graph of B versus n from the equation.)

 

[cukitas2001]

Well i was thinking that exponential made sense since u is 4pi*10^-7 in the equation. The slope of this would be from the moving around the equation to $$n=\frac{1}{\mu*I}*B$$ right? since the graph was B vs. n then the slope would be the 1/uI?

 

[berkeman]

No, just because u is expressed in scientific notation, that doesn't suggest that the curve should be an exponential. u is a constant.

If you did not get a linear relationship between B and n, then my guess would be that the current in the solenoid was not constant. How did you set that constant current? Also, the equation B=unI carries with it some assumptions -- what are those assumptions, and how might those assumptions have been violated a bit in your experiment?


EDIT -- And BTW, how were you measuring the B field?

 

[cukitas2001]

The current was kept constant at 1.5A. We were using a LoggerPro software and a Vernier Magnetic Field Sensor to measure the B-field. To alter the turns/meter we would disconnect the circuit and reconnect it at a shorter length of the Slinky. Might assumption be effected by crappy resources in the physics lab? (Confused):shy:

 

[berkeman]

More likely the limitations of the formula that you were using. When that formula is given in a textbook or other source, they usually say that it is for a _________ solenoid? What effects would using a non-________ solenoid have?

 

[cukitas2001]

ideal...but to vary this much isn't it weird? Any suggestions on what i should do for calculating u from my graph?

 

[berkeman]

No, not just "ideal". Ideal in what way? And what were the dimensions of your Slinky as you varied from max to min length. And when you calculate the value of $$\mu$$ what do you think its relationship with $$\mu_0$$ should be?

 

[cukitas2001]

The length of the solenoid (Slinky) was 0.83meters and the number of turns in said length was 70 so the turns/meter were 84.3

In a length of 0.83m the magnetic field averaged at 0.097mT
0.70m 0.113mT
0.60m 0.130mT
0.50m 0.135mT
0.40m 0.140mT

u and u_0 should be related by some constant of propotionality no?

 

[berkeman]

The length of the solenoid (Slinky) was 0.83meters and the number of turns in said length was 70 so the turns/meter were 84.3

In a length of 0.83m the magnetic field averaged at 0.097mT
0.70m 0.113mT
0.60m 0.130mT
0.50m 0.135mT
0.40m 0.140mT

What was the diameter of the Slinky again (sorry if I missed it earlier in the thread)? What percentage of the length of the Slinky is it? What happens to the simplified formula for B(n) as that percentage changes?

http://en.wikipedia.org/wiki/Solenoids#Derivation_of_magnetic_field_around_a_long_solenoid

BTW, did you insert the probe into the middle of the solenoid for each number n?

u and u_0 should be related by some constant of propotionality no?

Correct. The ratio is usually denoted as $$\mu_R$$ . What is the value of $$\mu_R$$ for the lab environment that you were performing the experiment in?

 

[cukitas2001]

The TA had made the impression that this was a very simple lab so things didnt get as complicated as finding constant of proportionality according to conditions or having to worrying about diameter or percentages. And yes the magnetic field probe was placed in the center of the solenoid to measure the b-field