Magnetic Field Chapter 28
Using an electromagnet to collect and transport scrap metal at a steel mill.
Applications of Mag fields and forces • Entertainment industry depended on the magnetic recording of music and images on audiotape and videotape. • Although digital technology has largely replaced magnetic recording, the industry still depends on the magnets that control CD and DVD players and computer hard drives; • Magnets also drive the speaker cones in headphones, TVs, computers, and telephones. A modern car comes equipped with dozens of magnets • because they are required in the motors for engine ignition, automatic window control, sunroof control, and windshield wiper control. • Most security alarm systems, doorbells, and automatic door latches employ magnets.
What Produces a Magnetic Field? • One way is to use moving electrically charged particles, such as a current in a wire, to make an electromagnet. The current produces a magnetic field that can be used. (computer hard drive). • The other way to produce a magnetic field is by means of elementary particles (such as electrons) because these particles have an intrinsic magnetic field around them. That is, the magnetic field is a basic characteristic of each particle just as mass and electric charge (or lack of charge) are basic characteristics.
Definition of • We determined the electric field at a point by putting a test particle of charge q at rest at that point and measuring the electric force acting on the particle. • If a magnetic monopole were available, we could define in a similar way. Because such particles have not been found, we must define in another way, in terms of the magnetic force exerted on a moving electrically charged test particle.
A charged particle is fired through the point at which B is to be defined, using various directions and speeds for the particle and determining the force that acts on the particle at that point. After many such trials we would find that when the particle's velocity is along a particular axis through the point, force is zero. • For all other directions of ,the magnitude of where is the angle between the zero-force axis and the direction of .
Direction of F The right-hand rule
HALL EFFECT • A beam of electrons in a vacuum can be deflected by a magnetic field. Can the drifting conduction electrons in a copper wire also be deflected by a magnetic field? In 1879, Edwin H. Hall, then a 24-year-old graduate student at the Johns Hopkins University, showed that they can. • This Hall effect allows us to find out whether the charge carriers in a conductor are positively or negatively charged. Beyond that, we can measure the number of such carriers per unit volume of the conductor.
Figure 28-8a shows a copper strip of width d, carrying a current i whose conventional direction is from the top of the figure to the bottom. The charge carriers are electrons and, as we know they drift (with drift speed vd) in the opposite directior, from bottom to top.
A strip of copper carrying a current i is immersed in. (a) The situation immediately after the magnetic field is turned on. The curved path that will then be taken by an electron. (b) The situation at equilibrium, which quickly follows. Note that negative charges pile up on the right side of the strip, leaving uncompensated positive charges on the left. Thus, the left side is at a higher potential than the right side. (c) For the same current direction., if the charge carriers were positively charged
is cyclotron frequency because charged particles circulate at this angular speed in the type of accelerator called a cyclotron,
When the velocity of a charged particle is perpendicular to a uniform magnetic ﬁeld, the particle moves in a circular path in a plane perpendicular to B. The magnetic force FB acting on the charge is always directed toward the center of the circle.
The Van Allen radiation belts consist of charged particles(electrons and protons) surrounding the Earth in doughnut-shaped regions. The particles, trapped by the Earth’s non-uniform magnetic ﬁeld, spiral around the ﬁeld lines from pole to pole, covering the distance in just a few seconds. These particles originate mainly from the Sun, but some come from stars and other heavenly objects. For this reason, the particles are called cosmic rays. Most cosmic rays are deﬂected by the Earth’s magnetic ﬁeld and never reach the atmosphere. However, some of the particles become trapped; it is these particles that make up the Van Allen belts. When the particles are located over the poles, they sometimes collide with atoms in the atmosphere, causing the atoms to emit visible light. Such collisions are the origin of the beautiful Aurora Borealis, or northern Lights, in the northern hemisphere and the Aurora Australis in the southern hemisphere.
Magnetic Force on a current carrying conductor A flexible wire passes between the pole faces of a magnet. Without current in the wire, the wire is straight. With upward current, the wire is deflected rightward. With downward current, the deflection is leftward. The connections for getting the current into the wire at one end and out of it at the other end are not shown.
A curved wire carries a current A curved wire carrying a current I in a uniform magnetic ﬁeld. The total magnetic force acting on the wire is equivalent to the force on a straight wire of length L’ running between the ends of the curved wire.
A current-carrying loop of arbitrary shape A current-carrying loop of arbitrary shape in a uniform magnetic ﬁeld. The net magnetic force on the loop is zero.
Torque on a current carrying conductor No forces are acting on sides 1 and 3 because these sides are parallel to B. Forces are acting on sides 2 and 4, however.
A rectangular current loop in a uniform magnetic ﬁeld. The area vector A perpendicular to the plane of the loop makes an angle with the ﬁeld. The magnetic forces exerted on sides 2 and 4 cancel, but the forces exerted on sides 1and 3 create a torque on the loop.