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1 | Lecture 8 Magnetic Fields Ch. 29. | 17 | in a magnetic field. B is directed into |
Cartoon Magnesia, Bar Magnet with N/S | the paper. v. F. v. F. +. r. = qvBsin90o. | ||
Poles, Right Hand Rule Topics Permanent | F. Magnitude of F = qvB. Direction is | ||
magnets Magnetic field lines, Force on a | given by the RHR (right hand rule). v. x. | ||
moving charge, Right hand rule, Force on a | x. x. x. x. x. | ||
current carrying wire in a magnetic field, | 18 | Find the radius r and period of motion | |
Torque on a current loop Demos Compass, | for a + charge moving in the magnetic | ||
declinometer, globe, magnet Iron fillings | field B. Use Newtons 2nd Law. v. a. r. | ||
and bar magnets Compass needle array Pair | Radius of the orbit. Important formula in | ||
of gray magnets CRT illustrating electron | Physics. What is the period of revolution | ||
beam bent bent by a bar magnet - Lorentz | of the motion? Note the period is | ||
law Gimbal mounted bar magnet Wire jumping | independent of the radius, amplitude, and | ||
out of a horseshoe magnet. Coil in a | velocity. Example of simple harmonic | ||
magnet Elmo Polling. | motion in 2D. T is also the cyclotron | ||
2 | period. Cyclotron frequency. It is | ||
3 | \. | important in the design of the cyclotron | |
4 | accelerator. Of course, this is important | ||
5 | because today it is used to make medical | ||
6 | isotopes for radiation therapy. x. x. x. | ||
7 | Magnetic Fields. Magnetism has been | x. | |
around as long as there has been an Earth | 19 | Example: If a proton moves in a circle | |
with an iron magnetic core. Thousands of | of radius 21 cm perpendicular to a B field | ||
years ago the Chinese built compasses for | of 0.4 T, what is the speed of the proton | ||
navigation in the shape of a spoon with | and the frequency of motion? x. v. x. x. | ||
rounded bottoms on which they balanced | r. x. x. x. x. x. | ||
(Rather curious shape for people who eat | 20 | Use right hand rule to find the | |
with chopsticks). Certain natural rocks | direction of F. Negative Charge. +. Rotate | ||
are ferromagnetic – having been magnetized | v into B through the smaller angle f and | ||
by cooling of the Earth’s core. Show a | the force F will be in the opposite | ||
sample of natural magnetic rock. Put it | Direction a right handed screw will move. | ||
next to many compasses. | 21 | Suppose we have an electron . Which | |
8 | Magnetism’s Sociabilities. Magnetism | picture is correct? x. x. x. x. x. x. x. | |
has always has something of a mystic aura | x. yes. B. No. v. F. F. v. | ||
about it. It is usually spoken of in a | 22 | Example of the force on a fast moving | |
favorable light. Animal magnetism, | proton due to the earth’s magnetic field. | ||
magnetic personality, and now you can wear | (Already we know we can neglect gravity, | ||
magnetic collars, bracelets, magnetic beds | but can we neglect magnetism?) Magnetic | ||
all designed to make you healthier – even | field of earth is about 0.5 gauss. Convert | ||
grow hair. We do not have the same feeling | to Tesla. 1 gauss=10-4 Tesla. Let v = 107 | ||
about electricity. If you live near | m/s moving North. What is the direction | ||
electric power lines, the first thing you | and magnitude of F? Take B = 0.5x10-4 T | ||
want to do is to sue the electric company. | and v perpendicular B to get maximum | ||
9 | Compass and Declinometer. In 1600 | effect. (a very fast-moving proton). V x B | |
William Gilbert used a compass needle to | is into the paper (west). Check with | ||
show how it oriented itself in the | globe. Earth. | ||
direction of the north geographic pole of | 23 | Force on a current-carrying wire in a | |
the Earth, which happens to be the south | uniform magnetic field. When a wire | ||
magnetic pole of the Earth’s permanent | carries current in a magnetic field, there | ||
magnetic field. Show compass and | is a force on the wire that is the sum of | ||
declinometer. Each has a slightly | the forces acting on each charge that is | ||
magnetized needle that is free to rotate. | contributing to the current. B (Out of the | ||
The compass lines up with the component of | paper). +. vd is the drift velocity of the | ||
the magnetic field line parallel to the | positive charges. Cross sectional area A | ||
surface of the Earth. The declinometer | of the wire. F. vd. i. L. n = density of | ||
lines up with the actual magnetic field | positive mobile charges. Number of charges | ||
line itself. It says that the angle | = nAL. v is perpendicular to B. or. L is a | ||
between the field lines and the surface is | vector in the direction of the current i | ||
71 degrees as measured from the south. | with magnitude equal to the length of the | ||
Earth’s magnetic field Basically there are | wire. Also. | ||
two types of magnets: permanent magnets | 24 | Show force on a wire in a magnetic | |
and electromagnets Show field lines for a | field. Current down. Current up. Drift | ||
bar magnet. Show bar magnet surrounded by | velocity of electrons. | ||
compass needle array. | 25 | Torques on current loops. Electric | |
10 | Permanent Magnets. Bar magnet is a | motors operate by connecting a coil in a | |
model of a ferromagnetic material that can | magnetic field to a current supply, which | ||
be permanently magnetized. Other | produces a torque on the coil causing it | ||
ferromagnetic materials are cobalt and | to rotate. Normal. i. P. a. i. b. Above is | ||
nickel. The origin of magnetism in | a rectangular loop of wire of sides a and | ||
materials is due mostly to the spinning | b carrying current I and is in a uniform | ||
motion of the charged electron on its own | magnetic field B that is perpendicular to | ||
axis. There is a small contribution from | the normal n. Equal and opposite forces | ||
the orbital motion of the electron. Atomic | are exerted on the sides a. No forces | ||
origin of magnetic field. | exerted on b since i is parallel to B. | ||
11 | Permanent Magnets (continued). In | Since net force is zero, we can evaluate | |
ferromagnetic materials there are whole | torque at any point. Evaluate it at P. | ||
sections of the iron called domains where | Torque tends to rotate loop until plane is | ||
the magnetism does add up from individual | perpendicular to B. A=ab = area of loop. | ||
electrons. Then there are other sections | Multiply by N for N loops. | ||
or domains where contributions from | 26 | Galvanometer. | |
different domains can cancel. However, by | 27 | Magnetic dipole moment is called ? and | |
putting the iron in a weak magnetic field | is a vector. Recall that for Electric | ||
you can align the domains more or less | dipole moment p. How do you define the | ||
permanently and produce a permanent bar | direction of ? ? RHR. | ||
magnet as you see here. In nonmagnetic | 28 | Demo: show torque on current loop | |
materials the contributions from all The | (galvanometer). Can you predict direction | ||
electrons cancel out. Domains are not even | of rotation? Example. A square loop has N | ||
formed. | = 100 turns. The area of the loop is 4 cm2 | ||
12 | Magnetic field lines do not stop at | and it carries a current I = 10 A. It | |
surface. They are continuous. They make | makes an angle of 30o with a B field equal | ||
complete loops. Field lines for a bar | to 0.8 T. Find the magnetic moment of the | ||
magnet are the same as for a current loop. | loop and the torque. Demo: Show world’s | ||
13 | Magnetic field lines. Similarities to | simplest electric motor. (scratch off all | |
electric lines A line drawn tangent to a | insulation on one end) Scratch off half on | ||
field line is the direction of the field | the other end Momentum will carry it ? | ||
at that point. The density of field lines | turn (no opportunity for current to | ||
still represent the strength of the field. | reverse coil direction). | ||
Differences The magnetic field lines do | 29 | Electron moving with speed v in a | |
not terminate on anything. They form | crossed electric and magnetic field in a | ||
complete loops. There is no magnetic | cathode ray tube. Electric field bends | ||
charge on as there was electric charge in | particle upwards Magnetic field bends it | ||
the electric case. This means if you cut a | downwards. y. e. | ||
bar magnet in half you get two smaller bar | 30 | Discovery of the electron by J.J. | |
magnets ad infinitum all the way down to | Thompson in 1897. Show demo of CRT. E=0, | ||
the atomic level – Magnetic atoms have an | B=0 Observe spot on screen. 2. Set E to | ||
atomic dipole – not a monopole as is the | some value and measure y the deflection. | ||
case for electric charge. They are not | 3. Now turn on B until spot returns to the | ||
necessarily perpendicular to the surface | original position. This ratio was first | ||
of the ferromagnetic material. | measured by Thompson to be lighter than | ||
14 | Definition of magnetic Field. | hydrogen by 1000. 4 Solve for. | |
definition of a magnetic field The units | 31 | Chapter 28 Problem 18. An alpha | |
of B are or in SI units(MKS). This is | particle (q = +2e, m = 4.00 u) travels in | ||
called a Tesla (T). One Tesla is a very | a circular path of radius 5.00 cm in a | ||
strong field. A commonly used smaller unit | magnetic field with B = 1.60 T. Calculate | ||
is the Gauss. 1 T = 104 G (Have to convert | the following values. (a) the speed of the | ||
Gauss to Tesla in formulas in MKS) In | particle (b) its period of revolution (c) | ||
general the force depends on angle . This | its kinetic energy (d) the potential | ||
is called the Lorentz Force. | difference through which it would have to | ||
15 | In analogy with the electric force on | be accelerated to achieve this energy. | |
a point charge, the corresponding equation | 32 | Chapter 28 Problem 37. A 2.3 kg copper | |
for a force on a moving point charge in a | rod rests on two horizontal rails 2.4 m | ||
magnetic field is: Consider a uniform B | apart and carries a current of 60 A from | ||
field for simplicity. Magnitude of | one rail to the other. The coefficient of | ||
Direction of F is given by the right hand | static friction between rod and rails is | ||
rule (see next slide). If the angle | 0.51. What is the smallest magnetic field | ||
between v and B is ? = 0, then the force = | (not necessarily vertical) that would | ||
0. v. sin(0o) = 0. F = 0. B. If ? = 90, | cause the rod to slide? (a) magnitude and | ||
then the force = and the particle moves in | direction. | ||
a circle. | 33 | Chapter 28 Problem 47. A circular coil | |
16 | Use right hand rule to find the | of 130 turns has a radius of 1.50 cm. (a) | |
direction of F. Positive Charge. +. Rotate | Calculate the current that results in a | ||
v into B through the smaller angle f and | magnetic dipole moment of 2.30 A·m2. (b) | ||
the force F will be in the direction a | Find the maximum torque that the coil, | ||
right handed screw will move. | carrying this current, can experience in a | ||
17 | Motion of a point positive charge “ ” | uniform 20.0 mT magnetic field. | |
Lecture 8 Magnetic Fields Ch.ppt |
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