# Electricity and Magnetism

Electricity and magnetism is an interesting aspect of electricity. We are familiar with in our everyday lives with the phenomenon of static cling - when two objects, such as a piece of Saran wrap and a wool sweater, are rubbed together, they cling. One feature of this that we don't encounter too often is static "repulsion" - if each piece of Saran wrap is rubbed on the wool sweater, then the pieces of Saran wrap will repel when brought near each other. These phenomena are interpreted in terms of the objects acquiring an electric charge, which has the following features:

• There are two types of charge, which by convention are labelled positive and negative.
• Like charges repel, and unlike charges attract.
• All objects may have a charge equal to an integral number of a basic unit of charge.
• Charge is never created or destroyed.

Electric Fields
A convenient concept for describing these electricity and magnetism forces is that of an electric field. Imagine that we have a fixed distribution of charges, such as on the plate below, and bring in the vicinity of this distribution a test charge Q.

Figure 1 Test charge in the presence of a fixed charge distribution

This charge will experience a force due to the presence of the other charges. One defines the electric field of the charge distribution as:

The electric field is a property of this fixed charge distribution; the force on a different charge Q' at the same point would be given by the product of the charge Q' and the same electric field. Note that the electric field at Q is always in the same direction as the electric force.

Because the force on a charge depends on the magnitude of the charges involved and on the distances separating the charges, the electric field varies from point to point, both in magnitude and direction. By convention, the direction of the electric field at a point is the direction of the force on a positive test charge placed at that point. An example of the electric field due to a positive point charge is given below.

Figure 2: Electric field lines of a positive charge

Power and Magnetic Fields
An electricity and magnetism phenomenon apparently unrelated to power are electrical magnetic fields. We are familiar with these forces through the interaction of compasses with the earth's magnetic field, or through fridge magnets or magnets on children's toys. Magnetic forces are explained in terms very similar to those used for electric forces:

• There are two types of magnetic poles, conventionally called North and South
• Like poles repel, and opposite poles attract
However, this attraction differs from electric power in one important aspect:
• Unlike electric charges, magnetic poles always occur in North-South pairs; there are no magnetic monopoles.
Later on we will see at the atomic level why this is so.

As in the case of electric charges, it is convenient to introduce the concept of a magnetic field in describing the action of magnetic forces. Magnetic field lines for a bar magnet are pictured below.

Figure 3: Magnetic field lines of a bar magnet

One can interpret these lines as indicating the direction that a compass needle will point if placed at that position.

The strength of magnetic fields is measured in units of Teslas (T). One tesla is actually a relatively strong field - the earth's magnetic field is of the order of 0.0001 T.

Magnetic Forces On Moving Charges
One basic feature is that, in the vicinity of a magnetic field, a moving charge will experience a force. Interestingly, the force on the charged particle is always perpendicular to the direction it is moving. Thus magnetic forces cause charged particles to change their direction of motion, but they do not change the speed of the particle.

This property is used in high-energy particle accelerators to focus beams of particles which eventually collide with targets to produce new particles.

Another way to understand these electricity and magnetism forces is to realize that if the force is perpendicular to the motion, then no work is done. Hence these forces do no work on charged particles and cannot increase their kinetic energy.

If a charged particle moves through a constant magnetic field, its speed stays the same, but its direction is constantly changing. A device in which this property is used is the mass spectrometer, which is used to identify elements. A basic mass spectrometer is pictured below.

Figure 4: Mass spectrometer

In this device a beam of charged particles (ions) enter a region of a magnetic field, where they experience a force and are bent in a circular path. The amount of bending depends on the mass (and charge) of the particle, and by measuring this amount one can infer they type of particle that is present by comparing to the bending of known elements.

Magnet Power From Electric Power
A connection was discovered (accidentally) by Orsted over 100 years ago, who noticed that a compass needle is deflected when brought into the vicinity of a current carrying wire. Thus, currents induce in their vicinity magnetic fields. An electromagnet is simply a coil of wires which, when a current is passed through, generate a magnetic field, as below.

Figure 5: Electromagnet

Another example of electricity and magnetism at work is in an atom, since an electron is a charge which moves about the nucleus, in effect it forms a current loop, and hence a magnetic field may be associated with an individual atom. It is this basic property which is believed to be the origin of the magnetic properties of various types of materials found in nature.

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