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# Magnetism Study Guide

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## Introduction

There is a strong connection between the electric and magnetic fields.  In this lesson, we will discuss magnetic materials, magnetic forces, motion of a charge in magnetic field, and magnetic field created by an electrical current.

## Magnetic Materials, Magnetic Field, and Magnetic Forces

What properties do refrigerator magnets have in common with Earth? First, the medium around each of them is characterized by a certain property called a magnetic field. A magnetic field manifests itself by the interaction between the magnet producing the field and other magnets or iron-based objects that might be in the vicinity. Any magnet, regardless of shape, has two poles: a north pole and a south pole. If you divide the magnet into two pieces, each of the pieces will also display the properties of north and south poles. Further reducing the size of the magnet does not separate the poles but keeps a north and a south pole in each of the pieces.

Some materials are naturally magnetic (for example, magnetite discovered to be magnetic for the first time about 2,000 years ago), and others can be magnetized (for example, iron-based objects), and still others will never display any magnetic properties. The existence of these categories is determined, as before with electrical charges, by the structure of the substance and the specific bonds between the atoms and molecules that are connected with each other.

Around a magnetic field, the magnetic properties can be described by the magnetic field lines, which are similar to the electric field lines. The direction of the magnetic field lines is from the N to the S pole outside the magnet and the other way inside the magnet (as shown in Figure 15.1 for a bar magnet).

The magnetic interaction, like that in the case of electrical charge interaction, is of two kinds: attraction and repulsion. The attraction force is established between two magnets facing each other with the different poles (N and S). The repulsion force is established between two poles of the same kind (N and N, or Sand S).

### Magnetic Force

The magnetic force is proportional to the strength of the magnetic field, to the velocity of the moving charge, and to the value of the charge.

F = q · v B

## Motion of a Point Charge in a Magnetic Field

Consider a point -like charge in a magnetic field. If the charge is in motion in the field, it can be shown that a force is acting on the charge that will curve the straight trajectory of the charge in the absence of any other interaction.

B is the value of the magnetic field at a point. This quantity is a vector because the magnetic field, similar to the electric field, has a definite direction. The unit for the magnetic field can be determined from the equation for magnetic force if we take only the scalar part of the magnetic force. Then you can see that magnetic field is measured in

This is a unit called a tesla (1 T) for Nicola Tesla (1856– 1943). A field of 1 T is a very large field (compare to the field of Earth, which is less than 10 –4 T). Therefore, the usual unit for magnetic fields is gauss (1 G).

1 G = 10–4T

The cross-product between the velocity and the magnetic field B can be interpreted in the following manner. To determine the magnetic force, you should consider only the speed perpendicular to the magnetic field, hence the magnetic force value is:

F = q · v · B · sin α

where α is the angle between the velocity v and magnetic field B.

If you construct a plane that contains both the velocity and the magnetic field, the resultant magnetic force is perpendicular to the field, whereas the direction (up or down) is given to the sign of the charge. See Figure 15.2.

The rule to determine the direction of the force is called the right-hand rule or the corkscrew rule.

In the case of the corkscrew for a positive charge, as shown in Figure 15.2, if you rotate the screw so that the velocity vector becomes superimposed on the magnetic field, the direction of advance of the screw is the direction of the force.

If the magnetic force is the net force on the particle, then the charge will be accelerated in the direction of the net force and the trajectory will be curved.

### Right-Hand Rule

Using the right hand, palm up, point the fingers in the direction of the vector magnetic field B and the thumb in the direction of the vector velocity v. The force will be perpendicular to the palm, and, if the charge is positive, the force will point upward. The force will be pointing downward if the charge, is negative.

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