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 Lecture 8 Magnetic Fields Ch \ Lecture 8 Magnetic Fields Ch Lecture 8 Magnetic Fields Ch Lecture 8 Magnetic Fields Ch Permanent Magnets Magnetic field lines do not stop at surface Use right hand rule to find the direction of F Use right hand rule to find the direction of F Show force on a wire in a magnetic field Show force on a wire in a magnetic field Torques on current loops Galvanometer Magnetic dipole moment is called Electron moving with speed v in a crossed electric and magnetic field
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## Lecture 8 Magnetic Fields Ch

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 Сл Текст Сл Текст 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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## Lecture 8 Magnetic Fields Ch

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