Physics 2225: Magnetic Fields
Purpose of this Minilab
• Learn about the shape and strength of the magnetic fields created by magnetic dipoles.
• Determine the strength of the Earth’s magnetic field.
Physics 2225: Magnetic Fields
The Concept of “Field” and “Field Lines”
The term “field” implies a region of space (or all of space)
Each location within this “field” has a specific property.
For example: In an “Electric Field” the property at each location in the field is the electric field vector
q
FE
charge of the small “test charge”
force on a “test charge”
Physics 2225: Magnetic Fields
Electric Field of a “Point Charge” Q
Q
A locationin the field
location)(at that E
Physics 2225: Magnetic Fields
Electric “Field Lines”
For electric fields, the property at each location in the fieldis a vector (has direction and magnitude).
When connecting the tangents to for different locations wecan create a map of “field lines”.
E
E
Field Lines (tangential to electric field vectors)
Physics 2225: Magnetic Fields
Electric Field Lines of a “Point Charge” Q
Notice:Looking at the “field lines”,
you can infer the direction of by looking at the directionof the field lines and,
you can infer the strength of by looking at the density of the field lines.
E
E
Physics 2225: Magnetic Fields
Electric Dipoles
Electric dipoles consist of two separate point charges.
Q1 Q2
Physics 2225: Magnetic Fields
Electric Dipole Field
For two point charges with equal but opposite charge the electric field looks like this:
Physics 2225: Magnetic Fields
Magnets
Magnetic monopoles have never been found: Magnets have two poles (“North and South poles”)
SN
If you cut the magnet in half, each half will still have two poles
SN SN
Physics 2225: Magnetic Fields
Magnetic Fields
To trace the direction of the magnetic field, a small test magnet (compass)can be used
Physics 2225: Magnetic Fields
Activity 1: Trace the Magnetic Field of a Horseshoe Magnet
Tape paperto table.
Use compassto map fieldlines. Drawthem on thepaper.
Draw on outline of the magneton the paper.
Physics 2225: Magnetic Fields
Activity 2: Trace the Magnetic Field of a Bar Magnet
Use the cork pin board
Back side has a cutoutfor the bar magnet
Insert barmagnet intocutout.Secure withblue maskingtape.
- Turn the board around. - Use pins to secure a sheet of paper. - Trace the field lines of the bar magnet on the paper using the compass.
Physics 2225: Magnetic Fields
Activity 3: Field Perturbation
Tape steel discnear the magnetat the bottom ofthe cork board.
Physics 2225: Magnetic Fields
Theoretical Field due to a Magnetic Monopole
34 r
rpB om
A
Tmspacefreeoftypermeabilio
7104
Physics 2225: Magnetic Fields
Superimpose Two Monopole Fields of Opposite Polarity to Get the Dipole Field Strength Along a Line as Shown
31
11 4 r
rpB om
32
22
)(
4 r
rpB om
pole #1 pole #2
L
compass
D
r1=D
r2=D+L
...),()(),(
:2Equation calculate
21 LDBDBLDB mm
Physics 2225: Magnetic Fields
Find Distance at which B(D,L) = BEarth
LD
????),(
such that D isWhat
EarthBLDB
),( LDB
Determine experimentally as follows using polar graph paper
Physics 2225: Magnetic Fields
1) Print polar graph paper.2) Place compass on graph paper (pivot in center).3) Rotate polar paper until compass needle points to 0°.
0°
90°
45°
Physics 2225: Magnetic Fields
4) Place bar magnet as shown with its axis in 90° direction.5) Move bar magnet until compass needle is deflected by 45°.
At that angle: BEarth=Bm
0°
90°
45°
move left or right
This is the distance D for which Bm=BEarth .
BEarth
Bm
Btotal
Physics 2225: Magnetic Fields
Do this procedure for all 4 possible configurations as shown here.Then get the average distance Dave of these four measurements.
0°
90°
45° 0°
90°
45°
0°
90°
45° 0°
90°
45°
Physics 2225: Magnetic Fields
Substitute BEarth and Dave into Equation 2
...),()(),(
:know now weD distance specific At the
...),()(),(
:2)(Equation magnet bar of field magnetic ofequation Previous
21
ave
21
LDBDBBLDB
LDBDBLDB
avemavemEarthave
mm
Physics 2225: Magnetic Fields
The Magnetic Moment of the Bar Magnet
L
pLm
magnetic moment of bar magnetmagnetic pole strength
Physics 2225: Magnetic Fields
Magnetic Moment in an External Magnetic Field
Bm
B
Magnetic moment in external field B experiences a torquethat acts to align the magnetic moment with the field.
sinBm (No torque if magnetic moment is aligned with the field).
m
Physics 2225: Magnetic Fields
If Magnet is Free to Rotate, an Oscillation Occurs
B
B
Torque on magnet rotates magnettowards alignment with the field…..but it overshoots to the otherside, like a pendulum….
pivot point
Once the magnet has reached theother extreme position, it rotatesback towards alignment, but willovershoot again….
The magnet oscillates between these two extreme positions.
Physics 2225: Magnetic Fields
The Period of this Oscillation
K
IT 2
22
12
:magnet theof inertia ofmoment
CAM
I
K = m B = p L B
A
C
m = magnetic momentB = external magnetic field
Physics 2225: Magnetic Fields
Measuring Period T in Earth’s Magnetic Field
ceiling
3.596 s
Start/Stop
Reset
Use stopwatch tomeasure period T
Physics 2225: Magnetic Fields
Calculating BEarth
EarthBLp
I
K
IT 22
oave21 , L , D , p offunction a...),()( LDBDBB avemavemEarth
Two equations with two unknowns: p, BEarth
Solution: Solve first equation for p, then plug result into second equation.Then solve for that equation for BEarth.
measured
known
measured
Calculated from measurements of M, A, C
measured