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Magnetic
Fields
Chapter 21
History of Magnetism

In 1269, Pierre de Maricourt of
France found that the directions
of a needle near a spherical
natural magnet formed lines that
encircled the sphere and passed
through two points diametrically
opposite each other, which he
called the poles of the magnet.
Subsequent experiments showed
that every magnet, regardless of
its shape, has two poles, called
North (N) and (S) poles, that
exert forces on other magnetic
poles similar to the way electric
charges exert forces on one
another. That is, like poles (N-N or
S-S) repel each other, and
opposite poles (N-S) attract
each other
Magnetic Fields

In our study of electricity, we described the
interactions between charged objects in terms of
electric fields. Recall that an electric field
surrounds any electric charge. In addition to
containing an electric field, the region of space
surrounding any moving electric charge also
contains a magnetic field. However, magnetic
field lines never end on a charge… they form
closed loops!
Magnetic vs. Electric Fields
Earths Magnetic Field Lines
and Poles
Earth’s Poles
 When
we speak of a compass magnet
having a north pole and a south pole, it is
more proper to say that it has a “north
seeking” pole and a “south seeking” pole.
This wording means that the north seeking
pole points to the north geographic pole
of the Earth, whereas the south seeking
pole points to the south geographic pole.
Direction of the Earth’s
Magnetic Field
 The
direction of the Earth’s magnetic field
has reversed several times during the last
million years. Evidence for this reversal is
provided by basalt, a type of rock on the
ocean floor. As the lava cools, it solidifies
and retains a picture of the Earth’s
magnetic field direction
Magnetic Field


We can define a magnetic field, B, at some
point in space in terms of the magnetic force,
F, the field exerts on a charged particle
moving with a velocity v, which we call the
test object.
For the time being, let’s assume no electric or
gravitational fields are present at the location
of the test object. Experiments on various
charged particles moving in a magnetic field
give the following results.
Properties of the magnetic
force on a charged particle
moving in a magnetic field



The magnetic F of the magnetic force
exerted on the particle is proportional to the
charge q and to the speed v of the particle.
When a charged particle moves parallel to
the magnetic field vector, the magnetic force
acting on the particle is zero
When the particles velocity vector makes any
angle Θ ≠ 0 with the magnetic field, the
magnetic force acts in a direction
perpendicular to both v and B; that is, F is
perpendicular to the plane formed by v and
B.
Properties of the Magnetic
Force Continued
 The
magnetic force exerted on a positive
charge is in the direction opposite the
direction of the magnetic force exerted
on a negative charge moving in the same
direction.
 The magnitude of the magnetic force
exerted on the moving particle is
proportional to sin theta, where theta is
the angle the particle’s velocity vector
makes with the direction of B.
Vector Expression for the
Magnetic Force on a Charged
Particle moving in a magnetic
field
Magnitude of the magnetic
force on a charged particle
moving in a magnetic field.
Right Hand Rule
SI Unit of Magnetic Field - Tesla
 The
SI unit of magnetic field is the newton
per coulomb-meter per second, which is
called the tesla (T).
 1𝑇
𝑁
= 1(
𝑚
𝐶∗ 𝑠
)
 Because
a coulomb per second is
defined to be an ampere:
 1𝑇
=1
𝑁
(
)
𝐴 ∗𝑚
Example - Velocity Selector
 In
many experiments involving moving
charged particles, it is important that all
particles move with essentially the same
velocity, which can be achieved by
applying a combination of an electric
field and a magnetic field oriented
perpendicularly to it.
Example - Velocity Selector
 When
the magnitudes of the two fields
are chosen so that qE = qvB, the charged
particle is modeled as a particle in
equilibrium and moves in a straight
vertical line through the region of the
fields. From the expression qE = qvB, we
find that:
 𝑣 = 𝐸/𝐵
Example – Mass Spectrometer
A
particle moving through a uniform
magnetic field perpendicular to its
direction of motion will be forced into
uniform circular motion
=qvB
mv = qB
r
If you know r and q you can measure the mass…
Magnetic Force Acting on a
Current Carrying Conductor

If a magnetic force is exerted on a single charged
particle when the particle moves through a
magnetic field, it should not surprise you that a
current-carrying wire also experiences a force
when placed in a magnetic field. The current is a
collection of many charged particles in motion;
hence, the resultant force exerted by the field on
the wire is the vector sum of the individual forces
exerted on all charged particles making up the
current. The force exerted on the particles is
transmitted to the wire when the particles collide
with the atoms making up the wire.
Force on a segment of
current-carrying wire in a
uniform magnetic field
𝐹𝐵 = 𝐼𝐿 𝑥 𝐵
Torque on a Current Loop in a
Uniform Magnetic Field
 Earlier
we showed how a
magnetic force is exerted on a
current-carrying conductor
placed in a magnetic field. With
that as a starting point, we now
show that a torque is exerted on
a current loop placed in a
magnetic field.
𝜏 = 𝐼𝐴 𝑥 𝐵
Example - The Hall Effect
 When
a current-carrying conductor is
placed in a magnetic field, a potential
difference is generated in a direction
perpendicular to both the current and the
magnetic field.
 This phenomenon, first observed by Edwin
Hall (1855-1938) in 1879, is known as the
Hall effect.