Download Magnetic Field and Force

Lab 5: Magnetic Field & Force
Objectives: to produce magnetic field by current flow in line, coil, and solenoid geometries;
to see that Bfields encircle electric current in a direction given by a right-hand-rule;
to verify that the magnetic field strength decreases with distance from the current;
to measure the effect (Force) of magnetic field on an electric current (not its source);
to practice the right-hand-rule to find direction for the Lorentz Force F = (qv) × B ;
to observe magnetic Force decrease rapidly with distance, since magnets are dipoles
Apparatus:
wire, coil, solenoid; bar magnets, disk magnets;
Equipment: compasses, DC Power Supply, Ammeter
Background: A moving charge produces a Magnetic Field that “circulates” around it,
in a right-hand screw direction: as a positive Q moves forward into page,
the magnetic field B encircles it clockwise. The B-field is more intense
close to the moving charge, and less intense in front of it and behind it:
BQv = o Qv sin / 4 r 2 .
The 4 r 2 in the source formula shows that B is a field intensity (per Area), reported in
Tesla [T] = [Ns/Cm] = [Js/Cm2] , so its flux thru Area B·A has units [J/A] = [Weber]
... which shows Energy due to current. But the magnetic field encircles a flow, it does
not diverge from positive (nor converge to negative) charge; so the total B·A thru any
closed surface (enclosing Volume) always adds up to zero. (“no magnetic monopoles,
just axial dipoles”). This means that magnetic field lines “always” form a closed loop.
At any place, the B vector produced by any one moving charge adds to
the Bfield vectors contributed by all other moving charges (tail-to-tip).
For an electric current I in a line with length ℓ , replace Qv with Iℓ .
For current in a straight wire, distance d from the place-of-interest (box)
all the “nearby” current contributes B out of page there with Qv = I 2d .
{this is an integration result that calc students might want to verify…}
Effectively, more distant current (beyond 45° from the | ) doesn’t help.
The Bfield for all parts of a current loop reinforce inside the loop,
so B is intense there, with length ℓ =N·2 r . But on the outside, the
B contributed by the near (↑) current is partly cancelled by the far
side (↓) current’s contribution, so the B-field is less intense outside
… lines of B-field are concentrated inside the loop, but are spread
out (so less intense field) outside the current loop.
The longer any particular B-field line is, the weaker the field intensity along that loop
(Ampere’s Law):  B·ℓ = μo  Ipiercing . ; I pierces the Area enclosed by the B-field line.
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Magnetic fields deflect moving charges, according to Lorentz Force
F = (qv) × B where the Force direction is given by the right-hand rule
(for cross-products, like torque was): the Force is perpendicular to v
(and also | to B). The moving charge shown would curve to the left,
with constant speed as it changed direction, along a circle around B .
A row of charges would form a loop of current ( qv = Iℓ ) , encircling an Area pierced
by B . Although the charges themselves do not gain Energy in a
magnetic field, the strong magnetic field that their loop will produce
is opposite the direction of the original B-field which they encircle. It
is their loop’s magnetic moment orientation which has Energy, as
magnetic torque can do Work if the loop flipped over : E = B·μ = B NIA cos θ .
Electromagnets are stronger if the atoms in it (iron core inside its coils, and the return
yoke outside them, can be magnetically oriented. To have most atoms oriented alike, it
should take more Energy to flip the magnetic moment (dis-orienting it) than what it has
in thermal Energy kBT . The atoms in a ferromagnetic material have large magnetic
moments so that they often cause each other to orient the same way, even with no
external field applied. In these permanent magnets, all the individual magnetic moment
vectors add up, and the magnet can be treated as if it has a North pole and a South pole.
All the magnetic flux BA that exits from N enters into S ; this has the same external
magnetic field pattern as a solenoid (current loops stacked lengthwise).
Activity 1. Magnetic Field Near a Straight-Wire Current
A. Earth-Field Comparison
With Power Supply “OFF”, connect a plain wire from PS (+) to PS (–). Current causes
magnetism – set the voltage knob high; adjust the Current Limit knob LOW.
With PS “off”, move a compass under the middle of the wire; check that there are no
magnetic anomalies near there. Slide some paper under the compass, and draw the
compass direction caused by Earth’s (ambient horizontal component) magnetic field.
Use a Right-Hand-Rule to predict the direction of the B-field that will be produced by
the current in the wire – orient the wire so that its B-field is perpendicular to Earth’s B.
Turn PS “on”, and adjust the current to deflect the compass noticeably (at least 45 );
draw this compass direction. Record current: _______ ____ do not adjust, switch OFF.
use a protractor to measure compass deflection angle _____ 
(caused by adding the current’s Bx to Earth’s By component)
If they are , then they are two legs of a right triangle;
knowing Earth’s horizontal By here _______ [Tesla],
deduce Bx,exp’t that must have been produced by the current.
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B. Theoretical B-Field Strength
Estimate the distance from the wire’s center
to the middle of each compass needle arm.
use this diagram (with I into page) as a guide
to show your estimated distances.
Calculate the theoretical magnetic field caused by the current at the estimated distance.
Then determine the horizontal component of the field
(not the upward diagonal vector B shown on diagram).
C. Experimental B-field strength Estimate by Oscillation Time Period
Turn ON the PS (at the previous I setting) and time 10-20 compass needle oscillations
Turn PS “OFF” and time the oscillations in Earth’s field (54[μT]) only (with I=0) .
I [A]
N
time [s]
T [s]
(fI2/ fo2)
f [osc/sec]
---------Did your compass needle oscillate quicker with the P.S. “on”? _______
The restoring torque on the compass needle is due to the horizontal magnetic field,
so for small-angle oscillations, 2 , and f 2 , will be proportional to Bx-y .
This means that Bon / Boff = (fon2/ foff2) , so we should also compute that squared ratio.
If wire B-field vector contribution is perpendicular to Earth’s , Bwire2 + BEarth2 = Bboth2 .
Solving for our desired unknown , Bwire2 = Bon2 – BEarth2 = BEarth2 ( (Bon / BEarth )2 –1)
… finally, this estimate for Bwire = 54[μT] ((fon2/ foff2)2 –1) = _________ ____ .
How close are your two experimental B values to each other?
to your theory estimate?
Activity 2. Magnetic Force on a Long Bar Magnet Caused by a Current Coil
Make a long bar magnet by carefully attaching a neodymium disk magnet
to each end of a long iron bar. Hang the magnet from a spring scale,
with North end downward, and note its weight: mg =_______ _____ .
Set the multi-turn flat coil on blocks above the table, with its axis vertical.
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Number of loops in coil N = _________ _____ ; coil radius r = ________ _____
Determine the current direction to produce B down thru coil center
(use a right-hand-rule) and connect the PS to it, that way. Sketch =>
Secure the spring scale so the bar magnet bottom pole is directly in the coil center.
Turn on the Power supply, and adjust current to obtain a few spring scale readings.)
Icoil[A]
spring F
Fmag= (F–mg) [N]
Bcoil_center = oNI/2r
Ignoring the top magnet pole, Fmag ≈ (BA)magnet  Bcoil … is it proportional to I ?
Now send the current the other direction thru the coil and repeat the same currents
Icoil[A]
spring F
Fmag= (F–mg) [N]
oNI/2r
Set the coil current to pull down on the magnet, with the bottom end at the coil center.
For large current I = ______ ___ , vary magnet height above coil center (0 to 150mm)
hmagnet [
]
spring F [N]
Fmag= (F–mg) [N]
Fmag/ Fh=0
Graph this Force data as a function of distance along the axis of the coil.
Theory derives B(h) = o NI /2(R2 + h2)³ ; measure the magnet length d =______ ___
and compute the % error we made by ignoring the magnet’s top pole (in non-zero B!) :
at h=0 , the Force on the bottom pole was { 1 + (R2)³ /(R2 + d2)³ }Fmag = ______[N]
at hmax , Force on bottom pole was { 1+ (R2 + h2)³ /(R2 + (h+d)2)³ } Fmag = _____[N]
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Activity 3. Solenoid Magnetic Field– A . Gradient
Connect the big copper solenoid to the PS, and stand it on the table, with axis vertical.
Hang the disk magnet from spring scale, with axis vertical; weight mg :_______ ____.
Adjust PS current to I = ____ ___; slowly lower magnet into the attracting solenoid,
while watching the spring Force scale. Where is the attraction strongest? ___________
Is it difficult to keep the magnet in the solenoid’s centerline axis? _________________
What is the attraction at the solenoid’s exact center? _______________________
A magnet is a di-pole, so it experiences non-zero net Force only if the field is different
at its two ends … Force depends on the external field gradient (B/d).
What do your observations imply about how uniform the solenoid’s field is?
B. Solenoid B –Field Torque
Move the disk magnets onto the short iron bar, and clip the string onto the bar middle.
Dangle the short bar magnet near the solenoid top opening. Adjust current and describe
the bar’s behavior.
By hand, turn the bar slowly to the opposite orientation (opposite end up).
What orientation for the bar requires maximum torque (by you) to turn it?
Show by sketch (label North pole, South pole, and B arrow)
how even a perfect uniform field applies torque to a magnet.
C. Solenoid Magnetic Field – Outside
A compass needle (like your short bar magnet) tries to orient itself in the direction of
the local B-field. Lay the solenoid on its side next to a spacer block ; use a compass to
follow along a “line of magnetic field” from solenoid North end to solenoid South end.
A line that exits at the N coil edge gets how far from the coils at its midpoint?
Does that N coil edge line return into the solenoid at the South coil edge?
Measure the solenoid’s length ________ ____ and radius ________ ____ .
.
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Lab 5 Summary Sheet
Name :_______________________
Lab Partner : _____________
1. Discuss experimental and theoretical magnetic fields from 1A and 1B and 1C .
2. Did the magnetic Force on this magnet seem to be proportional to current?
Consider the theory formula for magnetic field due to a coil at height h along its axis ;
explicitly show how the formula predicts a simple “2R” for small h :
show all steps in finding the B(h) formula for “very large” h :
3. The textbook derivation for the field at the center of the solenoid claims that the field
outside the solenoid is zero, yet you mapped a non-zero field.
What Area at the solenoid center (inside) did the magnetic field pierce (out toward N)?
What Area (outside) at solenoid midpoint did the magnetic field pierce (in toward S)?
The B-field on the outside should be how many times as weak , as the B at the center?
Comment … how many digits will this approximate textbook formula get right?
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