Download Chapter 28. Magnetic Field

Chapter 28. Magnetic Field
28.1. What is Physics?
28.2. What Produces a Magnetic Field?
28.3. The Definition of Magnetic Field
28.4. Crossed Fields: Discovery of the
Electron
28.5. Crossed Fields: The Hall Effect
28.6. A Circulating Charged Particle
28.7. Cyclotrons and Synchrotrons
28.8. Magnetic Force on a Current-Carrying
Wire
28.9. Torque on a Current Loop
28.10. The Magnetic Dipole Moment
What is Physics?
Permanent magnets
• A magnet has two poles, a north pole and a south pole
• No Magnetic monopole available in nature.
The magnetic forces
Like poles repel each other, and unlike
poles attract.
The magnetic field
• A magnetic field exists in the region around a magnet.
The magnetic field is a vector that has both
magnitude and direction.
• The direction of the magnetic field at any point in
space is the direction indicated by the north pole
of a small compass needle placed at that point.
The magnetic field line
• The lines originate from the north pole and end on the
south pole; they do not start or stop in midspace.
• The magnetic field at any point is tangent to the
magnetic field line at that point.
• The strength of the field is proportional to the number
of lines per unit area that passes through a surface
oriented perpendicular to the lines.
• The magnetic field lines will never come to cross each
other.
What Produces a Magnetic Field?
• Moving electrically charged particles, such as a current,
produce a magnetic field
• Permanent magnet. Elementary particles such as electrons
have an intrinsic magnetic field around them. The magnetic
fields of the electrons in certain materials add together to
give a net magnetic field around the material. Such addition
is the reason why a permanent magnet has a permanent
magnetic field. In other materials, the magnetic fields of
the electrons cancel out, giving no net magnetic field
surrounding the material
Magnetic force on a Charged Particle
When a charge is placed in a magnetic field, it
experiences a magnetic force if two conditions are
met:
1. The charge must be moving. No magnetic force acts on
a stationary charge.
2. The velocity of the moving charge must have a
component that is perpendicular to the direction of the
field.
Magnetic force on a Charged Particle
Right-Hand Rule
The force
acting on a charged
particle moving with velocity
through
a magnetic field
is always
perpendicular to
and
.
Check Your Understanding
Two particles, having the same charge but different velocities, are
moving in a constant magnetic field (see the drawing, where the
velocity vectors are drawn to scale). Which particle, if either,
experiences the greater magnetic force? (a) Particle 1
experiences the greater force, because it is moving perpendicular
to the magnetic field. (b) Particle 2 experiences the greater
force, because it has the greater speed. (c) Particle 2 experiences
the greater force, because a component of its velocity is parallel
to the magnetic field. (d) Both particles experience the same
magnetic force, because the component of each velocity that is
perpendicular to the magnetic field is the same.
Example 1 Magnetic Forces on Charged
Particles
A proton in a particle accelerator has a
speed of 5.0×106 m/s. The proton
encounters a magnetic field whose
magnitude is 0.40 T and whose direction
makes an angle of θ =30.0° with respect
to the proton’s velocity. Find (a) the
magnitude and direction of the magnetic
force on the proton and (b) the
acceleration of the proton. The Mass of
proton is 1.67x10-27 kg.
The Definition of Magnetic Field
• The magnetic field B is a vector, and its direction is
direction is along the zero-force axis.
• The magnitude B of the magnetic field at any point
in space is defined as
where F is the magnitude of the magnetic force on a
positive test charge q0 , v is the velocity of the charge
which makes an angle  with the direction of the
magnetic field.
• SI Unit of Magnetic Field:
Differences of ELECTRIC AND
MAGNETIC FIELDS
1. Direction of forces
– The electric force on a charged particle (both
moving and stationary) is always parallel (or
anti-parallel) to the electric field direction.
– The magnetic force on a moving charged particle
is always perpendicular to both magnetic field
and velocity of the particle. No magnetic force
on a stationary charged particle.
2. THE WORK DONE ON A CHARGED
PARTICLE:
–
–
The electric force can do work on the
particle.
The magnetic force cannot do work and
change the kinetic energy of the
charged particle.
Crossed Fields: Discovery of the Electron
1. Set and to zero and note the position of the spot on
screen S due to the undeflected beam.
2. Turn on and measure the resulting beam deflection y.
3. Maintaining , now turn on and adjust its value until
the beam returns to the undeflected position. (With the
forces in opposition, they can be made to cancel.)
Crossed Fields: The Hall Effect
Can the drifting conduction electrons in a copper wire
also be deflected by a magnetic field?
the magnitude of that potential
difference is
When the electric and magnetic forces
are in balance
E v B
d
A  ld
V
i

B
d neld
Sample Problem 28
Figure 28-9 shows a solid metal cube, of edge length
d=1.5cm, moving in the positive y direction at a constant
velocity of magnitude 4.0 m/s. The cube moves through a
uniform magnetic field of magnitude 0.050 T in the
positive z direction.
• (a) Which cube face is at a lower electric potential and
which is at a higher electric potential because of the
motion through the field?
• (b) What is the potential difference between the faces
of higher and lower electric potential?
The motion of a charged particle in a
constant magnetic field
• A charged particle in a
constant magnetic field will
do uniform circular motion
• The radius of the circle is
Check Your Understanding
Three particles have
identical charges and masses.
They enter a constant
magnetic field and follow the
paths shown in the drawing.
Rank the speeds of the
particles, largest to smallest.
Example 3 The Motion of a Proton
A proton is released from rest at point
A, which is located next to the positive
plate of a parallel plate capacitor (see
Figure 21.13). The proton then
accelerates toward the negative plate,
leaving the capacitor at point B through
a small hole in the plate. The electric
potential of the positive plate is 2100 V
greater than that of the negative plate,
so VA–VB=2100 V. Once outside the
capacitor, the proton travels at a
constant velocity until it enters a region
of constant magnetic field of magnitude
0.10 T. The velocity is perpendicular to
the magnetic field, which is directed out
of the page in Figure 21.13. Find (a) the
speed vB of the proton when it leaves
the negative plate of the capacitor, and
(b) the radius r of the circular path on
which the proton moves in the magnetic
field.
Helical Paths
If the velocity of a charged particle has a component parallel to the (uniform)
magnetic field
, the particle will move in a helical path about the direction of
the field vector.
The Auroral
The Cyclotron
Proton Synchrotron
Magnetic Force on a Current-Carrying Wire
Magnetic Force on a Current-Carrying Wire
• If the magnetic field is not
perpendicular to the wire, as in
Fig, the magnetic force is given
by
Define
as a length vector that has magnitude L and is directed along the
wire segment in the direction of the (conventional) current.
Check Your Understanding
The same current-carrying wire is placed in the same
magnetic field B in four different orientations (see
the drawing). Rank the orientations according to the
magnitude of the magnetic force exerted on the wire,
largest to smallest.
Sample Problem 28
A straight, horizontal length of copper wire has a
current i=28 A through it. What are the magnitude
and direction of the minimum magnetic field
needed to suspend the wire—that is, to balance the
gravitational force on it? The linear density (mass
per unit length) of the wire is 46.6 g/m.
Torque on a Current Loop
Fnet  0
the vector , which is normal to the plane of the coil
with direction determined by right hand rule shown in
fig. (b).
   iAB sin 
A is area of loop
When a current-carrying loop is placed in a magnetic field, the loop
tends to rotate such that its normal becomes aligned with the
magnetic field
Torque on a Current coil
A coil containing N loops, each of area A, the force on
each side is N times larger, and the torque on the coil
becomes:
The Magnetic Dipole Moment of Coil
• The direction of
is that of the normal vector to
the plane of the coil and thus is given by the same
right-hand rule. That is, grasp the coil with the
fingers of your right hand in the direction of current
i; the outstretched thumb of that hand gives the
direction of .
• The magnitude of
is given by
N is the number of turns in the coil, i is the current through the
coil, and A is the area enclosed by each turn of the coil.
Magnetic Dipole in a Magnetic Field
• The torque on the coil due to a magnetic field
• The magnetic potential energy
•If an applied torque to rotates a
magnetic dipole from an initial
orientation to another
orientation , then work Wa is done
on the dipole by the applied torque is
Example The Torque Exerted on a
Current-Carrying Coil
A coil of wire has an area of 2.0×10–4 m2, consists of
100 loops or turns, and contains a current of 0.045 A.
The coil is placed in a uniform magnetic field of
magnitude 0.15 T. (a) Determine the magnetic moment
of the coil. (b) Find the maximum torque that the
magnetic field can exert on the coil.
A DC electric motor
Conceptual Questions
1. A charged particle, passing through a certain region of space,
has a velocity whose magnitude and direction remain constant.
(a) If it is known that the external magnetic field is zero
everywhere in this region, can you conclude that the external
electric field is also zero? Explain. (b) If it is known that the
external electric field is zero everywhere, can you conclude
that the external magnetic field is also zero? Explain.
2. Suppose that the positive charge in Figure 21.10a were launched
from the negative plate toward the positive plate, in a direction
opposite to the electric field. A sufficiently strong electric
field would prevent the charge from striking the positive plate.
Suppose the positive charge in Figure 21.10b were launched
from the south pole toward the north pole, in a direction
opposite to the magnetic field. Would a sufficiently strong
magnetic field prevent the charge from reaching the north
pole? Account for your answer.
3. Three particles move through a constant magnetic
field and follow the paths shown in the drawing.
Determine whether each particle is positively
charged, negatively charged, or neutral. Give a
reason for each answer.
4. When one end of a bar magnet is placed near a TV
screen, the picture becomes distorted. Why?
5.
A positive charge moves along a circular path under
the influence of a magnetic field. The magnetic
field is perpendicular to the plane of the circle, as
in Figure 21.12. If the velocity of the particle is
reversed at some point along the path, will the
particle retrace its path? If not, draw the new
path. Explain.