• Did everybody get the detailed comments on their first lab report from ELMS?
• Lab 1 resubmit due 26 Nov
• Bring paper copy of lab report for today’s lab to class next week

• Learn how to measure magnetic fields
• Verify Biot-Savart law/Ampere’s Law by comparing prediction and measurement for various current configurations
• Learn how to use a hall probe
• Do lots of error propagation

Easy to make a magnetic field using a current dB


4

0
Idl
 r
ˆ r
2 rhat is a unit vector pointing from the bit of current dl to the place at which you want to calculate the field.
B field is perpendicular to the current and the vector pointing from the current to the point where the field is being calculated.

Infinite wire
B


0
2

I r

0

4
 
10

7 

Electric dipole
“magnetic dipole”

D0 at Fermilab http://www-d0.fnal.gov/solenoid/

B


0
NI
2

R
G0 magnet at Jefferson Lab http://www.jlab.org
superconducting toroid
B( D L)  1.6 T-m

a
40 a a=10 cm
30
20
10
-25 -20 -15 -10 -5
0
0 x (cm)
5 10 15 20
B


0
NI
2

 a

2  a
2
 
2
2
3 /

2
 a

2  x a
2
 
2
2
3

/ 2


25 polarized 3 He lab at NIST http:/www.nist.gov
B  25 gauss
B
 x

0


 
4

3
5
2

0
NI
0 a dB dx x

0
 d 2 B dx 2 x

0

0

Note: only the component of B perpendicular to the current is measured!

What is the size of the potential?
Force on the current is zero when the force due to the electric field cancels out the force due to the magnetic field

d

d


d

d

d


V

IB nqt
To get something big enough to measure, you want to make I and B as big as possible, t as small as possible.
B=1T, I=10A, t=0.0008 m (thinnest wire that can carry 10A).
For copper, n=5x1028 m -3 , q=1.6x10
-19 C
V

 28   
19 
0.0008

1.6 10

6
V
Pretty small!

• orientation of probe important
• zeroing of scale important
• calibration of probe important

•
Calibrate the gauss meter before using it. Some are broken! This is your chance to check!
• Set meter to calibrate, read calibration constant on the probe, and adjust large metal screw until you get that reading
• Turn to measure and zero using the black zero knob
• flip back and forth between calibrate and measure a few times to verify your calibration is stable.
The tips of these probes are very fragile! These probes are very expensive! That’s why you have to double up. Please, please, please, please, please be gentle with them!

Assume all other systematic errors are small compared to the measurement of the B field.
The manual for the Hall Probe meter gives a
4% systematic error on the linearity for this device.

Need to double up on this lab!

B vs I at center of coil
B

N

0
I
2 a
Fit B vs I. Verify the intercept is consistent with zero. Extract N from the slope. Take into account the random errors and the syst error on
B as you did last week. (random errors go into the fit: systematic error is calculated for the slope, not for the data points, and is added in quad with the error on the slope due to random errors from the fit)

B vs x at fixed I (read carefully in your lab manual about what happens if you don’t have your center position quite right)
B

N

0
I a
2
2 ( a
2  x
2 3 / 2
)
 
3
2 ln( a
2  x
2
)
 ln(

0
NIa
2
2
) u
 ln( x
2  a
2
) and v=ln(B) v
 
3

2 u ln(

0
NIa
2
2
)
Fit u vs v. Verify slope is consistent with 3/2. Will extract N from intercept. But, need random errors in u,v to do fit.

v

 v


1
B B
 v


B
B

u
 ln( x
2  a
2

 u x
 x
2
2
 x a

 u a
 x
2
2
 a a
2
2
)
Be careful! The error on a is really a systematic error, since it is common for all values of u. Don’t include it in the errors you send when you are fitting u vs v!
 u
2 
1
( x
2  a
2 2
)
(4 x
2

2 x

4 a
2

2 a
)

b
 ln(

NIa
2
2
)
N

N
 b


2

Ia
2 e b
N ,


N


I I
N
,


N a


2 a
N

N

N
 b
2 


I
I 
2


2
 a a 
2

Add random errors on the intercept from fit in quad with sys error from B field.
(translate sys error in B field into sys error on v and propogate that into a sys error on the intercept using the formulas from last week.) NOTE: because
 ln B


B
B
 

B
A linearity error on B becomes a zeroing error in ln(B) when doing systematics
Then, calculate N and the error on N

skip

skip toroid

• note the formulas in this lab are in mks, not cgs. 1T = 10^4 g
•MAKE SURE THE AMMETER IS ON DC, NOT AC!!
• do not exceed 10 amps!
• take at least 10 data points
• You will blow a fuse on the ammeter if you use more than 10 amps!
•Read your lab manual carefully. Lots of important details in the instructions.
• keep your credit cards, etc away from magnet (watches, pdas, memory sticks)
• axial probe (round) for loops, transverse (flat with round plastic cover) for toroid
•open switch when not actually doing measurement: large currents can overheat the coil.
• when push button, allow for settling time
• to center, move the probe in and out and look for the position that gives maximum field
• for transverse probe (used for measuring toroid) need to rotate probe to get max b field reading before starting

•when doing linear fits, taking data so as to give the largest possible range in x values is very helpful!
• for toroid, be careful not to go into edges of coil
• for single coil, if you have the position of the center wrong, instead of a straight line, you will get one that bends back on itself. If you have this, adjust the center position until it is straight.

• When the lab manual says “reverse the direction of the current and see if the magnetic field reverses”, don’t do it. It’s not a good thing to do to an analogue meter.
• Don’t do 2 coils part (Part B)
• For toroid, ignore the last sentence of C1. Instead, measure from the inside the windings, through the windings, to outside of the windings. However, realize that only a small portion of the data (inside the windings, but not near the edge) will be useful for testing the equation in C.2.