8/4/08 Lecture 1 Part 2 1

The Magnetic Field

A magnet creates a field B(x).

An electric current creates a field B(x).(Oersted ; Ampère)

자기장—magnetic field—

8/4/08 Lecture 1 Part 2 2

The Magnetic Field

The field B inside and outside a magnet occurs because the iron atoms are similar to tiny current loops:

… both kinds of motion create a magnetic field similar to Ampère’s law

자기장—magnetic field—

8/4/08 Lecture 1 Part 2 3

Example: A long straight wire with current I

Tm/A 104

ˆ2

70

0

φBrI

Andre-Marie Ampère(1775-1836)

Advanced Calculus진보된 미적분학

Idl 0B

8/4/08 Lecture 1 Part 2 4

Compare B due to a bar magnet and B due to the Earth

8/4/08 Lecture 1 Part 2 5

Magnets and Forces

►Magnets exert forces on each other.

► But there is another, very fundamental magnetic force:The magnetic field exerts a force on any charged particle that moves across the field lines.

What will happen?

F = q v x B (magnetic force on q)

Compare: F = q E, the electric field force

8/4/08 Lecture 1 Part 2 6

Interaction between a magnetic field and an electric current

The magnetic field between North and South magnet poles —

The field is approximately uniform, if the two poles are close together.

8/4/08 Lecture 1 Part 2 7

If a charged particle moves across a magnetic field …

… there is a force in the direction perpendicular to the velocity vector.

8/4/08 Lecture 1 Part 2 8

The Cyclotron, and other particle accelerators

Design:

The 60-inch cyclotron built by E. O. Lawrence (1941); used by the Manhattan Project; the discovery of Plutonium.

/1/ The magnetic field B causes the particles to cycle (circular motion) in the dees./2/ The alternating electric field E causes the particles to gain kinetic energy in the gap.

8/4/08 Lecture 1 Part 2 9

Bevatron:Proton Synchrotron built by E. O. Lawrence (1954); discovery of the antiproton by Segrè and Chamberlain.

Fermilab Tevatron ColliderProton-antiproton collisions at √s = 2 TeV.

8/4/08 Lecture 1 Part 2 10

Place a straight wire carrying electric current across a magnetic field.

There is a force on the wire, perpendicular to the wire.

8/4/08 Lecture 1 Part 2 11

Place a loop of wire carrying electric current in a magnetic field.

There is a torque on the wire, which can produce an angular acceleration of the loop.

8/4/08 Lecture 1 Part 2 12

—electric motor—

Electric Motors 전동기 Basic design principle: The rotor is an electromagnet. Torque on the electromagnet drives the rotation.

8/4/08 Lecture 1 Part 2 13

—electric motor—

Electric Motors 전동기

The most common type of electric motor for alternating current is an induction motor. The magnetic field rotates; and the electric current in the rotor is induced by Faraday’s Law.(Invented by Nikola Tesla – 1888)

8/4/08 Lecture 1 Part 2 14

Two-Phase Induction MotorIn the two-phase motor, two sets of coils are set perpendicular to each other surrounding the core. When alternating current is sent to the coils, they become electromagnets where polarity rapidly changes with each reversal of current flow. As the first coils are supplied with current, they create a magnetic field which starts the core turning. When the first coils' current supply reverses, the second coil set is at its maximum supply point and creates its own magnetic field; the core spins on. In effect the "magnetization" amount never varies and a rotating magnetic filed is created. The result is a smooth-running, commutator-free motor with the rotor as its only moving part.

http://www.fi.edu/learn/case-files/tesla/motor.html

Nikola Tesla