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Magnetic Fields
Chapter 26
26.2 The force exerted by a magnetic field
Definition of B
26.3 Motion of a charged particle in a magnetic field
A circulating charged particle
Crossed fields: discovery of the electron
The cyclotron and mass spectrometer
Magnetic force on currents
Using integration
The Hall effect, Hall potential
26.4 Magnetic force on a current-carrying wire
Wire segment of length L carrying
current I. If the wire is in a
magnetic field, there will be a force
on each charge carrier resulting in a
force on the wire.
26.4 Magnetic force on a current-carrying wire
Flexible wire passing between pole
faces of a magnet.
(a) no current in wire
(b) upward current
(c) downward current
CHECKPOINT: the figure shows a current I
through a wire in a uniform magnetic field B,
as well as the magnetic force FB acting on
the wire. The field is oriented so that the
force is maximum. In what direction is the
A: upwards (+y)
B: downwards (-y) Answer: downwards (or –y direction)
C: -z direction
EXERCISE: A wire segment 3 mm long
carries a current of 3 A in the +x
It lies in a magnetic field of magnitude
0.02 T that is in the xy plane and
makes an angle of 30° with the +x
direction, as shown.
What is the magnetic force exerted on
the wire segment?
Torque on a current loop
The elements of an electric motor. The
current-carrying loop is free to rotate in
the magnetic field. Magnetic forces
produce a torque that rotates the loop.
The direction of the current is reversed
every half revolution so that the torque
always acts in the same direction.
If the conductor is not straight, we can divide it into
infinitesimal segments dl. The force on each segment is
Then we can integrate this expression along the wire to
find the total force on a conductor of any shape.
EXAMPLE: A wire bent in a semicircular
loop of radius R lies in the xy plane.
It carries a current I from point a
to point b. There is a uniform
magnetic field B perpendicular to
the plane of the loop. Find the force
acting on the semicircular loop part
of the wire.
Picture the problem: The force dF exerted on a segment of the
semicircular wire lies in the xy plane. We find the total force by
expressing the x and y components of dF in terms of  and
integrating them separately from  = 0 to  = 
More examples will be done on Wednesday after the Workshop
The Hall Effect – the separation of charge in a conducting wire
It results in a voltage VH called the Hall voltage. The sign of the charge
carriers can be determined by measuring the sign of the Hall voltage, and
the number of carriers per unit volume from the magnitude of VH.
The Quantum Hall Effects
In 1980, while studying the
Hall effect in
semiconductors at very low
temperatures and very large
magnetic fields, Klaus von
Klitzing discovered that the
Hall voltage is quantized.
(Nobel Prize in physics,
Further reading Tipler p 847
Sources of the Magnetic Field
The magnetic field of moving charges
The magnetic field of currents
Oersted’s experiment: he
showed that a compass
needle is deflected by an
electric current.
no current
current flows
Magnetic field lines
Magnetic field B can be represented by field lines, and as
with electric field lines, the direction of the field is
indicated by the direction of the field line, and the
magnitude of the field is indicated by the density of
There are two important differences:
1. Electric field lines are in the direction of the electric
force on a positive charge, but magnetic field lines are
perpendicular to the magnetic force on a moving charge.
2. Electric field lines begin on positive charges and end
on negative charges; magnetic field lines neither begin
nor end.