Purpose of this Minilab

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.


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

qFE

charge of the small “test charge”

force on a “test charge”


Electric Field of a “Point Charge” Q

Q

A locationin the field

location)(at that E


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)


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


Electric Dipoles

Electric dipoles consist of two separate point charges.

Q1 Q2


Electric Dipole Field For two point charges with equal but opposite charge the electric field looks like this:


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


Magnetic Fields

To trace the direction of the magnetic field, a small test magnet (compass)can be used


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.


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.


Activity 3: Field Perturbation

Tape steel discnear the magnetat the bottom ofthe cork board.


Part 2: Measure the Earth’s Magnetic Field


Theoretical Field due to a Magnetic Monopole

34 rrpB o

m

ATmspacefreeoftypermeabilio

7104


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


Find Distance at which B(D,L) = BEarth

LD

????),(such that D isWhat

EarthBLDB

),( LDB

Determine experimentally as follows using polar graph paper


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°


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


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°


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


The Magnetic Moment of the Bar Magnet

L

pLm

magnetic moment of bar magnetmagnetic pole strength


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


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.


The Period of this Oscillation

KIT 2

22

12

:magnet theof inertia ofmoment

CAMI

K = m B = p L B

AC

m = magnetic momentB = external magnetic field


Measuring Period T in Earth’s Magnetic Field

ceiling

3.596 s

Start/Stop

Reset

Use stopwatch tomeasure period T


Calculating BEarth

EarthBLpI

KIT 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

Purpose of this Minilab

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