III. Magnetism Fields produced mostly by moving charges acting on moving charges.

III–1 Magnetic Fields

Main Topics Introduction into Magnetism. Permanent Magnets and Magnetic Fields. Magnetic Induction. Electric Currents Produce Magnetic Fields. Forces on Electric Currents.

Introduction into Magnetism Magnetic and electric effects are known for many thousands years. But only in 19 th century a close relation between them was found. Deeper understanding was reached only after the development of the special theory of relativity in 20 th century. Studying of magnetic properties of materials has been up to now a field of active research.

Permanent Magnets I The mathematical description of magnetic fields is considerably more complicated then it is for the electric fields. It is worth to begin with good qualitative understanding of simple magnetic effects. It has been known for a long time that certain materials are capable of interacting by another long-distance force which is not electrostatic.

Permanent Magnets II This force had been named magnetic. This force can be either attractive or repulsive. The magnitude of this force decreases with distance. There had been a suspicion that electric and magnetic forces were the same thing. They are not! But they are related.

Permanent Magnets III The reason: magnets don’t influence charges at rest but they do influence moving charges. At first, the magnetic properties were attributed to some “magnetic charges”. Since both attractive and repulsive forces exist there must be two kinds of these “charges”. But it was found that these magnetic ”charges” can’t be separated!

Permanent Magnets IV If you separate a piece of any size and shape from a permanent magnet, it will always contain both “charges”. So they are called more appropriately – magnetic poles. Unlike poles attract and like poles repel. We expect that poles don’t switch without external influence and the interactions are stable.

A Simple Experiment The fact that unlike poles attract and like poles repel can be proved by a simple experiment using three magnets: Let’s mark one pole on each of the magnets. At least two of the magnets must have the mark on the same pole. We can find them using the interaction with the third magnet. We readily see e.g. that marked poles repel.

Permanent Magnets V Around any magnet there is magnetic field which can interact with other magnets. In pre-physics ages it was found that the Earth is a source of a magnetic field. It is a large permanent magnet. A magnetic needle would always point in the North-South direction.

Permanent Magnets VI This is a principle of compass, used by the Chinese thousands years ago for navigation. A convention has been accepted: the pole of a magnet pointing to the North geographic pole is called the north and the other one the south. the magnetic field has the direction from the north to the south. i.e. in the direction a compass would point, which enables a simple calibration of magnets.

Permanent Magnets VII From this it is clear that the south magnetic pole of the Earth is near to the North geographical pole. A compass doesn’t point exactly to the north. It has a declination which depends on the particular location since magnetic and geographic poles dont coincide. The field is even not horizontal. Magnets can be imagined consisting of smaller magnets so the convention works even inside them.

Magnetic Fields I Similarly as in the case of electric fields, we accept an idea that magnetic interactions are mediated by magnetic fields. Every source of magnetic field e.g. magnet spreads (by the speed of light) around an information on its position, orientation and strength. This information can be received by another source. The results is that a force between those sources appears.

Magnetic Fields II As can be easily proved by a magnetic needle, magnetic fields generally change directions and therefore must be described in every point by some vector quantity. Magnetic fields are vector fields. Magnetic fields are usually described by the vector of the magnetic induction.

Magnetic Fields III The magnetic field lines are: lines tangential to the magnetic induction in every point. closed lines which pass through the space as well as through the magnets in the same direction as a north pole of a magnetic needle would point – from north to south.

Magnetic Fields IV Since magnetic monopoles don’t exist, the magnetic field lines are closed lines and outside the magnets they resemble the electric field lines of an electric dipole. Although it is in principle possible to study directly the forces between sources of magnetic fields, it is usual to separate problems to how fields are produced how they interact with other sources.

Electric Currents Produce Magnetic Fields I First important step to find relations between electric and magnetic fields was the discovery done by Hans Christian Oersted ( , Danish) in He found that electric currents are sources of magnetic fields. A long straight wire produces magnetic field whose field lines are circles centered on it.

Electric Currents Produce Magnetic Fields II It is interesting that these closed field lines exist as if they were produced by some invisible magnets! Magnetic field due to a circular loop of wire is torroidal (doughnut). The direction of the field lines can be found using a right-hand rule. Later we shall see where this rule comes from and how these and other fields look in more detail and quantitatively.

Forces on Electric Currents I When it was found that electric currents are sources of magnetic fields it could have been expected that magnetic fields also exert force on currents-carrying wires. The interaction was also proved by Oersted and a formula for a force on a wire of carrying the current I was found: (cross product)cross product

Forces on Electric Currents II For a long straight wire which can be described by the vector carrying the current I the integral formula is valid: If currents produce magnetic fields and they are also affected by them it logically means that currents act on currents by magnetic forces.

Forces on Electric Currents III Now, we can qualitatively show that two parallel currents will attract them selves and the force will be in the straight line which connect these currents. This seems to be similar to a force between two point charges but now the force is the result of a double vector product as we shall see soon.

Forces on Electric Currents IV From the formula describing force on electric currents the units can be derived. The SI unit for the magnetic induction B is 1 Tesla, abbreviated as T, 1T = 1 N/Am Some older are units still commonly used for instance 1 Gauss: 1G = T

Homework Chapter 27 – 1, 2, 6, 10, 14, 15, 19, 20

Things to read and learn This Lecture Covers : Chapter 27 – 1, 2, 3 Advance Reading : Chapter 28 – 1, 2, 3, 4, 6 Try to understand all the details of the vector product of two vectors!

The vector or cross product I Let Definition (components) The magnitude of the vector Is the surface of a parallelepiped made by.

The vector or cross product II The vector is perpendicular to the plane made by the vectors and and must form a right-turning system.  ijk = {1 (even permutation), -1 (odd), 0 (eq.)} ^