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III. Magnetism

Explore the basics of magnetism, magnetic fields, and permanent magnets. Understand how electric currents produce magnetic fields and learn about the forces acting on electric currents.

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III. Magnetism

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

  2. III–1 Magnetic Fields

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

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

  5. Permanent Magnets I • The mathematical description of magnetic fields is considerably morecomplicated 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 a long-distance force.

  6. Permanent Magnets II • These forces had been named magnetic. • These forces can be both attractive and repulsive. • The magnitude of these forces decreases with distance. • There had been a suspicion that electric and magnetic forces were the same thing. They are not! But they are related.

  7. Permanent Magnets III • The reason: magnets don’t influencenon-moving 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 was found that these magnetic ”charges” can’t be separated!

  8. 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. • Around a magnet we imagine a magnetic field which can interact with other magnets.

  9. Permanent Magnets V • 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. • This is a principle of compass, known by the Chinese more than a thousand years ago and used for navigation.

  10. Permanent Magnets VI • A convention has been accepted that the pole of a magnet pointing to the North geographic pole would be called the north and the other one the south and the magnetic field will have the direction from the north to the south.

  11. 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. • Magnets can be imagined consisting of smaller magnets so the convention works even inside them.

  12. 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.

  13. 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 inductionB.

  14. 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 the magnets in the same direction as a north pole of a magnetic needle would point – from north to south.

  15. 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 and how they interacts with other sources.

  16. Electric Currents Produce Magnetic Fields I • First important step to find relations between electric and magnetic fields was the discovery done by Oersted (Hans Christian) in 1820. 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.

  17. Electric Currents Produce Magnetic Fields II • It is interesting that these closed field lines exist like if they were due to invisible magnets! • Magnetic field due to a circular loop of wire is torroidal. • We shall study these and other fields in more detail and quantitatively later.

  18. 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 dl carrying the current I was found: dF = I(dl x B) (cross product)

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

  20. 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.

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

  22. Things to read and learn • Chapter 27 – 1, 2, 3 • Try to understand all the details of the vector product of two vectors!

  23. The vector or cross product I Let c=a.b Definition (components) • The magnitude |c| Is the surface of a parallelepiped made by a,b.

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

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