# Magnetic fields

## The Magnetic Dipole Moment

The Magnetic Dipole Moment We can describe the current-carrying coil of the preceding section with a single  vector ji, its magnetic dipole moment. We take the direction of je to be that of the normal vector n 10 the plane of the coil, as in We define the magnitude of Ii as.         …

## Torque on a Current Loop

Torque on a Current Loop Much of the world’s work is done by electric motors. The forces behind this work are the magnetic forces that we studied in the preceding section-that is, the forces  that a magnetic field exerts on a wire that carries a current.Figure 29-20 shows a simple motor, consisting of a single current-carrying …

## Magnetic Force on a Current-Carrying Wire

Magnetic Force on a Current-Carrying Wire We have already seen (in connection with the Hall effect) that a magnetic field exerts a sideways force on electrons moving in a wire. This force must then be transmitted to the wire itself, because the conduction electrons cannot escape sideways out of the wire. In Fig. 29-16a, a vertical wire, carrying …

## The Cyclotron

The Cyclotron Figure 29-15 is a top view of the region of a cyclotron in which the particles (protons, say) circulate. The two hollow D-shaped objects (open on their straight edges) are  made of sheet copper. These dees, as they are called are part of an electrical oscillator that alternates the electric potential difference across the gap …

## Cyclotrons and Synchrotrons

Cyclotrons and Synchrotrons What is the structure of matter on the smallest scale? This question has always . intrigued physicists. One way of getting at the answer is to allow an energetic charged particle (a proton, for example) to slam into a solid target. Better yet, allow two such energetic protons to collide head-on. Then analyze the debris …

## A Circulating Charged Particle

A Circulating Charged Particle If a particle moves in a circle at constant speed, we can be sure that the net force acting on the particle is constant in magnitude and points toward the center of the circle, always perpendicular to the particle’s velocity. Think of a stone tied to a string and whirled in a circle on …

## Crossed Fields The Hall Effect

Crossed Fields  The Hall Effect As we just discussed, 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 …

## Crossed Fields: Discovery of the Electron

Crossed Fields: Discovery of the Electron Both an electric field  E and a magnetic field Ii can produce a force on a charged particle. When the two fields are  perpendicular to each other, they are said to be crossed fields. Here we shall examine what happens to charged  articles-  -namely.e>electrons-as they move through crossed fields. We …

## The Deftnition Of B

The Definition Of B We determined the electric, field E at a point by putting a test particle of charge q at rest at th~t point and measuring the electric force FE acting on the particle. W~ then defined E as If a magnetic monopole were available, we could define Ii in a similar way. Because such …

## The Magnetic Fieldmm

The Magnetic Field We have discussed how a charged plastic rod produces a vector field-the electric field E -at all points in the space around it. Similarly, a magnet produces a vector field-the magnetic field B-at all points in the space around it. You get a hint 01 that magnetic field whenever you attach a note to …