Download Chapter 20: Magnetism

Chapter 20
LECTURE NOTES
Magnetism
In ancient times, rocks were found that attracted iron in Magnesia (part of Asia Minor). It was
found that these permanent magnets or lodestones would always point north if suspended.
Every magnet has a north pole and a south pole. There are no magnetic monopoles. Like poles
repel and unlike poles attract. N repels N, S repels S, but N and S attract each other.
The pole of a suspended magnet that points north is called the north (N) or north-seeking pole.
Thus the earth must have a south magnetic pole near the north geographic pole and a north
magnetic pole near the south geographic pole. The magnetic poles are offset by hundreds of
miles from the geographic poles.
A magnetic field surrounds every magnet. We can picture the field lines as arrows pointing in
the direction an isolated N pole would travel. There are no isolated poles in nature; this
definition is simply a convention paralleling the test charge that traces an electric field.
The earth’s magnetic field resembles a dipole field like the one around a common bar magnet.
We believe it is created by a dynamo effect due to the rotation of the earth stirring currents in the
molten metal conducting outer core. A compass needle points to the magnetic pole so we must
correct our readings for declination (the magnetic pole is not at geographic north). We can also
observe the dip of a compass needle as a component of the earth’s field angles downward toward
the pole.
B due to current carrying wire
For nearly two centuries we have known electric currents create magnetic fields. If we place a
current carrying wire in an external magnetic field B it will experience a force of magnitude F =
I  B sin  . This defines B the magnetic field strength (also known as magnetic induction) as
B=
Fmax
.
I
Here F is the force in newtons felt by the wire of length  carrying current I at an angle  to the
external magnetic field B. Fmax refers to the force when  = 90°. The units for B are
N
1N
which we call a tesla: 1 tesla (T) =
.
Am
Am
Many electromagnetic variables and units have been used over the past few centuries. One still
sees magnetic field strengths given in gauss (G) where 1T = 10,000G. The strength of the
earth’s magnetic field is about 0.5G or 5 x 10-5T. The strongest continuous field lab magnets are
around 60T.
Chapter 20
LECTURE NOTES
Lorentz Force
A positively charged point particle q (in coulombs) moving with velocity v (in m/s) through a
region of space in which a magnetic field B (in tesla) and electric field E (in N/m) exists will in
general feel a force F = qE + qv x B.
The magnetic force has the unusual property that it is directed perpendicular to the plane of both
v and B as implied by the vector cross product above.
v
The magnetic force is qvBsin  in the direction (for
a + charge) of the thumb when the fingers of the
right hand curl from v to B (here into the page).

B
Example
A proton (charge + 1.6 x 10-19 C) is shot upward at v = 3 x 106 m/s. This is almost perpendicular
to the earth’s 5 x 10-5T magnetic field at our location. Find the magnetic force on the proton and
its subsequent motion.
The force is qvB = 2.4 x 10-17 N and this is initially directed west. As the particle begins to
move west, the force stays constant in magnitude neglecting any collisions but changes direction
to down, then east, then up. (Try to reproduce this using the right hand rule for v x B).
Evidently the proton circles about earth’s magnetic field lines. The magnetic force qvB provides
mv
the centripetal force so qvB = mv2/r or r =
= .626m. This is the radius of the circle the
qB
proton travels in (using m = 1.67 x 10-27kg).
Force on a current carrying wire in an external magnetic field
We have already seen the force on a current carrying straight wire is F = I  B sin θ. Consider the
current to be composed of individual positively charged particles with velocity in the direction of
the conventional current. Each particle feels the qv x B force and transmits this to the wire as a
whole. Thus the direction of the force is given by the usual right hand rule as I x B. The fingers
of the right hand point in the direction of the conventional current. Curl them toward B and the
thumb points in the direction of the force.
If the wire is bent into a loop it feels a torque τmax = NIAB where the torque τ is N ۰ m, N is the
number of turns or loops, I is the current in amps, A the area of the loop in m2 and B the
magnetic field strength in tesla. This is the basis for an electric motor.
Chapter 20
LECTURE NOTES
Magnetic field produced by a current – carrying wire.
A moving charge produces a magnet field of its own. Ampere’s law which we will introduce
 I
later can show B = 0 is the magnetic field strength (in tesla) a distance r (in m) from a wire
2 r
carrying current I (in amps). The constant μ0 = 4 x 10-7T m/A is the permeability of free space.
Currents flowing through house wiring can produce fields comparable to that of the earth a few
cm from the wire. The magnetic field is seen to circle the wire in a direction given by another
right hand rule: point the thumb in the direction of conventional flow, and the fingers will curl in
the direction of B.
 0 NI
N
where
is the number of


loops or turns per unit length. This is a solenoid (or electromagnet), which is often used as a
switch. The direction of B is that of the thumb of the right hand when the fingers curl in the
direction of conventional current flow.
If the current carrying wire is bent into a loop, we find B =
Force between two current carrying wires
Since each current carrying wire creates its own B field, we expect the wires to exert forces on
F  II
each other as any magnet would. We find  o 1 2 where F/  is the force (in N) per unit

2r
length (in m) exerted on a wire, I1 and I2 are the currents (in A) of the two wires, and r (in m) is
the center-to-center separation of the wires. The force is repulsive when the currents flow in
opposite directions and attractive for currents in the same direction.
Note: The coulomb is defined in terms of the amperes, which is one of the seven fundamental SI
quantities. l A is defined as the current in each of 2 parallel wires 1m apart which results in a
force of 2 x 10-7N/m on each wire. Then we let 1C = 1 A ۰ S.
Example
Two parallel wires a distance 20.0 cm apart carry
oppositely directed currents of 4.00A and 5.00A
respectively. Find the net magnetic field strength due
I1
•
I2
to these currents at the midpoint between the wires and the force per unit length each wire exerts
on the other.
 0 I1
= 8 μT, into the plane of the paper.
2 r1
Let I2 = 5.00A and r2 = .100m. Then B2 = 10μT, also into the plane of the paper.
Let I1 = 4.00A and r1 = .100m. Then B1 =
B = B1 + B2 = 18μT, into the plane of the paper.
Chapter 20
LECTURE NOTES
The force per unit between the wires is repulsive and of magnitude
4  10 7 Tm
 II
2  10 5 N
A ( 4A)( 5A)
F/  = 0 1 2 
.

2r
2(.200m)
m
Hall Effect
As charges move through a conductor held in an external B field, they feel a sideway (v x B)
force causing a charge separation and a potential difference. Soon the E field, created by the
potential difference, exerts an electric force canceling the magnetic force. This effect is used in
many instruments to detect and measure magnetic fields.
Atomic explanation of magnetism
Electrons can be pictured as spinning on their axis; this motion of a charge generates a magnetic
field. For ferromagnetic materials unpaired electrons in inner subshells align their spins and
create a net magnetic field over a microscopic domain. When the magnetic fields of the domains
are aligned (perhaps because they were placed in an external magnetic field) the whole material
becomes a strong magnet.
The domains can be disordered and the magnetism lost. Heating disorders things, and, above the
Curie temperature, one cannot make a magnet.
Paramagnetic materials are usually attracted by a strong external field. This effect is due to
orbital electron motion.
Diamagnetic materials are usually repelled by a strong external field due to the orbital direction
of electrons being affected by the external field.
When a piece of iron is placed inside a solenoid, the magnetic field is much stronger than due to
NI
the current alone. This is called an electromagnet where B =
with μ a characteristic of the

material inside the coil.
SUMMARY OF RIGHT HAND RULES:
1.
Force on positively charged particle moving with velocity v in magnetic field B. Fingers
point in v direction, curl to B; thumb is F.
2.
Force on current (I) carrying straight wire is magnetic full B. Fingers point in
conventional I direction, curl to B; thumb is F.
3.
Magnetic field direction created by current (I) carrying straight wire. Thumb points in
conventional I direction, fingers curl in B direction when you grasp the wire.
4.
Magnetic field created by current (I) carrying wire loop or solenoid. Curl fingers in
conventional I direction; thumb points in direction of B.