PERMANENT MAGNETS 2/13/2017 HORSESHOE MAGNET BAR MAGNET. Magnetic interaction. Magnetic interaction. Another way of stating this is that

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UNT 5 Magnetism and Electromagnetic nduction AP PHYSCS 2 Over 2,500 years ago, ancient Chinese civilization

iron. CHAPTER 17 MAGNETSM They soon learned that these rocks could be hung from a string and used for navigation.

each other, they repel each other. f you bring opposite poles near each other, they attract each other.

f you break a magnet into two pieces, each piece still has two poles a north pole and a south pole.

1 UNT 5 Magnetism and Electromagnetic nduction AP PHYSCS 2 Over 2,500 years ago, ancient Chinese civilization discovered that certain rocks - now called lodestones - will attract each other, as well as pick up small bits of iron. CHAPTER 17 MAGNETSM They soon learned that these rocks could be hung from a string and used for navigation. PERMANENT MAGNETS Magnetic interaction AR MAGNET HORSESHOE MAGNET f you bring the like poles of two magnets near each other, they repel each other. f you bring opposite poles near each other, they attract each other. N S N S Magnetic interaction Magnets always have two poles. f you break a magnet into two pieces, each piece still has two poles a north pole and a south pole. Another way of stating this is that there can be no magnetic monopoles The physical laws of magnetism prove that a single magnetic pole cannot exist. All magnets will always have both a North and a South pole. 1

Magnetic and electrical interactions are different Electrically charged objects do not interact with magnets in the same way

Magnetic Fields Just as electrically charged particles create an electric field in the space around them, magnets create a

COMPASS: small magnet that has the ability to rotate and always align with a magnetic field.

2 Magnetic and electrical interactions are different Electrically charged objects do not interact with magnets in the same way that magnets interact with magnets. Magnetic poles are not electric charges. Magnetic Fields Just as electrically charged particles create an electric field in the space around them, magnets create a magnetic field that distorts space around them. E How can we detect a magnetic field? We need a test magnet. COMPASS: small magnet that has the ability to rotate and always align with a magnetic field. A compass contains a tiny magnet on a lowfriction pivot. The north pole of a compass points toward geographic north; the south pole points toward geographic south. Magnetic interaction A compass measures the direction of a magnetic field! 2

3 What creates a Magnetic Field? oth orbital motion and the spinning motion of every electron in an atom produce magnetic fields. What creates a Magnetic Field? Magnetic fields are created by ELECTRCALLY CHARGED PARTCLES N MOTON! 2 The fundamental nature of all magnetism is the motion of charged particles. What materials can be magnetized? Nickel Cobalt ron How can you make a permanent magnet? Rub Fe-Ni-Co against a strong magnet Place Fe-Ni-Co in a strong magnetic field How can you make a permanent magnet weaker? Heat it Hit it SOURCES OF MAGNETC FELD Permanent Magnets Earth Current-carrying wires 3

SOURCE 1: PERMANENT MAGNETS (MAGNETC DOMANS) SOURCE 2: EARTH

! Domains before magnetization Domains after magnetization SOURCE

MAGNETC FELD Magnetic Field Lines The magnetic field lines of a

4 SOURCE 1: PERMANENT MAGNETS (MAGNETC DOMANS) SOURCE 2: EARTH (currents in the molten core of Earth) Clusters of aligned atoms!! Domains before magnetization Domains after magnetization SOURCE 3: Electric Current carrying wires Hans Christian Øersted ( ) t s all about the Øersteds. DRECTON OF MAGNETC FELD SOURCE 1: Permanent Magnets DRECTON OF MAGNETC FELD Magnetic Field Lines The magnetic field lines of a permanent bar magnet points from North to South. Easy way to remember: Magnetic fields fly South Mrs. Rawding 4

DRECTON OF MAGNETC FELD SOURCE 1: Permanent

needle will point on the direction of the magnetic

direction of the magnetic field at a particular

Direction of the magnetic field Magnets DRECTON

5 DRECTON OF MAGNETC FELD SOURCE 1: Permanent Magnets DRECTON OF MAGNETC FELD SOURCE 1: Permanent Magnets The north side of a compass needle will point on the direction of the magnetic field DRECTON OF MAGNETC FELD SOURCE 1: Permanent Magnets We can use a compass to detect the direction of the magnetic field at a particular location. Direction of the magnetic field DRECTON OF MAGNETC FELD SOURCE 1: Permanent Magnets DRECTON OF MAGNETC FELD SOURCE 2: Permanent Magnets AR MAGNET S N AR MAGNETS N S S N 5

DRECTON OF MAGNETC FELD SOURCE 2: Permanent Magnets AR MAGNETS

horseshoe magnet to generate a magnetic field with almost parallel

S N S N DRECTON OF MAGNETC FELD SOURCE 2: EARTH DRECTON OF MAGNETC

giant magnet, with its magnetic south pole close to its geographic

A current-carrying wire contains electrons in motion, and thus

6 DRECTON OF MAGNETC FELD SOURCE 2: Permanent Magnets AR MAGNETS DRECTON OF MAGNETC FELD SOURCE 1: Permanent Magnets We use a horseshoe magnet to generate a magnetic field with almost parallel field lines between the poles. S N S N DRECTON OF MAGNETC FELD SOURCE 2: EARTH DRECTON OF MAGNETC FELD SOURCE 3: Electric Current carrying wires Earth acts as a giant magnet, with its magnetic south pole close to its geographic north pole and its magnetic north pole close to its geographic south pole. DRECTON OF MAGNETC FELD SOURCE 3: Electric Current carrying wires A current-carrying wire contains electrons in motion, and thus creates a magnetic field! A currentcarrying wire creates a magnetic field that is in the shape of concentric circular loops around the wire! Magnetic Field () Electric current () 6

DRECTON OF MAGNETC FELD SOURCE 3: Electric Current carrying wires Charged objects in motion produce a magnetic field; stationary

The method for determining the shape of the field produced by the electric current in a wire is called the righthand rule.

Definition: Region where a magnetic force can be detected. Symbol: Units: Tesla (T) Type of PQ: ector = 0 ( 2 r) 1.

7 DRECTON OF MAGNETC FELD SOURCE 3: Electric Current carrying wires Charged objects in motion produce a magnetic field; stationary charged objects do not. The method for determining the shape of the field produced by the electric current in a wire is called the righthand rule. DRECTON OF MAGNETC FELD SOURCE 3: Electric Current carrying wires Your fingers will wrap around the way that the magnetic field wraps around the wire! Right Hand Rule # 1 Point the thumb of your right hand in the direction of the electric current PHYSCAL QUANTTY: MAGNETC FELD Definition: Region where a magnetic force can be detected. Symbol: Units: Tesla (T) Type of PQ: ector = 0 ( 2 r) 1. Alternating Current 2. Light 3. X-rays 4. Radio 5. Remote Control 6. Electric Motor 7. Robotics 8. Laser 9 Wireless Communications 10. Limitless Free Energy 11. Radar Working in Three Dimensions This is an arrow pointing This is an arrow pointing out of the page. into the page. (Think of the tip of an (Think of the tail of an arrow arrow pointing at you) pointing away from you) 7

8 WHTEOARD What does the magnetic field look like on each side of the wire? (into the paper) (out of the paper) WHTEOARD Draw the magnetic field lines that show the field surrounding the current-carrying wire. WHTEOARD Draw the magnetic field lines that show the field surrounding the current-carrying wire. The magnetic field will be tangent to the magnetic field lines Whiteboard Warmup Sketch the magnetic field of a loop of wire from a cross-sectional view. (magine a donut cut in half and looked at from the side) 8

9 Use RHR #1 for each section of the loop, and then use the Principle of Superposition! Superposition Whiteboard Two wires carrying equal currents are crossed, as shown above. Determine the magnetic field in each of the labeled regions. = 0 T Current Events Two parallel wires are each carrying a current of 0.8 Ampères upward, as shown below. Calculate the magnitude and direction of the magnetic field at points A, and C shown below. 10 cm 10 cm 6 cm 4 cm = 0 T μ 0 = 1.3 x 10-6 T*m/A 10 cm 10 cm 6 cm 4 cm = m 0 2pr ector superposition in the third dimension! The magnetic field produced by an electric current in a long straight wire The magnitude of the magnetic field at a perpendicular distance r from a long straight current-carrying wire is expressed as: straight wire = μ 0 2π wire r A = 2.2 x 10-6 T out of the page = 0 T C = 3.1 x 10-6 T out of the page The farther you move from the currentcarrying wire, the smaller the magnitude of the magnetic field. The greater the current, the larger the magnitude of the magnetic field. 9

10 Magnetic fields produced by a straight wire acuum/magnetic permeability The constant μ o is known as the magnetic permeability. t is used when calculating the magnetic field in a vacuum, although the value is approximately the same for air. μ is the magnetic permeability of a substance and replaces μ o if the magnetic field is being calculated inside a material. straight wire = μ 0 wire 2π r acuum permeability μ 0 = 4 x10 7 T m A WHTEOARD Magnetic fields produced by a loop or coil Find the magnitude of the magnetic field at a point located 0.8 m away from a long, straight, wire carrying an electric current of 2 A. = μ 0 wire 2π r = 5x10 7 T = μ 0 2r = Nμ 0 2r at center of loop at center of coil with N loops Magnetic field due to electron motion in an atom n an early model of the hydrogen atom, electron motion was depicted as a circular electric current. The magnetic field at the center of a currentcarrying loop of radius r is: = μ 0 2r This motion also describes a magnetic dipole moment for atoms, making this model potentially useful for explaining magnetic properties of materials. WHTEOARD n the early 20th-century model of the hydrogen atom, the electron was thought to move in a circle of radius 0.53x10 10 m, orbiting once around the nucleus every 1.5x s. Determine the magnitude of the magnetic field produced by the electron at the center of its circular orbit and its dipole moment. = μ 0 2r = 4 x x10 10 = T = q t = 1.6x10 19 C 1.5x10 16 s = ma 10

WHTEOARD Magnetic fields produced by a solenoid Draw the magnetic field lines of a solenoid connected to a battery.

bar magnet are very similar. MAGNETC FORCE ON AN ELECTRC CURRENT CARRYNG WRE DEO Wire coils with current are known as electromagnets.

then a magnetic field should exert a magnetic force on a current-carrying wire similar to the force it exerts on another magnet.

11 WHTEOARD Magnetic fields produced by a solenoid Draw the magnetic field lines of a solenoid connected to a battery. = N μ 0 L inside solenoid Current loops and bar magnets The field produced by the current in a loop or a coil and that produced by a bar magnet are very similar. MAGNETC FORCE ON AN ELECTRC CURRENT CARRYNG WRE DEO Wire coils with current are known as electromagnets. Magnetic force exerted by the magnetic field on a current-carrying wire f a current-carrying wire is similar in some ways to a magnet, then a magnetic field should exert a magnetic force on a current-carrying wire similar to the force it exerts on another magnet. A magnet sometimes pulls on a wire and sometimes does not the effect depends on the relative directions of the field and the current in the wire. RGHT HAND RULE #2 F 11

12 MAGNETC FORCE ON AN ELECTRC CURRENT CARRYNG WRE MAGNETC FORCE ON AN ELECTRC CURRENT CARRYNG WRE MAGNETC FORCE ON AN ELECTRC CURRENT CARRYNG WRE out of the paper 12

MAGNETC FORCE ON AN ELECTRC CURRENT CARRYNG WRE MAGNETC FORCE ON AN ELECTRC CURRENT CARRYNG WRE into the paper MAGNETC FORCE ON AN ELECTRC CURRENT CARRYNG WRE Magnetic force exerted on an electric

13 MAGNETC FORCE ON AN ELECTRC CURRENT CARRYNG WRE MAGNETC FORCE ON AN ELECTRC CURRENT CARRYNG WRE into the paper MAGNETC FORCE ON AN ELECTRC CURRENT CARRYNG WRE Magnetic force exerted on an electric current carrying wire The magnitude of the magnet force F onw that a uniform magnetic field exerts on a straight current-carrying wire of length L with current is F onw = L sin Where is the angle between the direction of the field and the current. The direction of this magnetic force is given by the right-hand rule for the magnetic force. Earth WHTEOARD F = 1.6 N = T = T WHTEOARD You wonder if instead of supporting your clothesline with two poles you could replace the poles and the clothes line with a current carrying wire in Earth s Magnetic field, which near the surface has a magnitude 5x10-5 T and points north. Assume that your house is located near the equator, where the field produced by Earth is approximately parallel to Earth s surface. The clothesline is 10 m long. The clothes and the line have a mass of 2 kg. What direction should you orient the clothesline? What current is needed to support it? s this a promising way to support the clothesline? 13

14 WHTEOARD - SOLUTON F = Lsin(θ) What will happen when you place an ECCLoop inside the magnetic field? = F Lsin(θ) F = F E on CL = m g Lsin(θ) = 39,200 A Torque exerted on a magnetic loop A magnetic field exerts forces of the current passing through the wires of a coil, resulting in a torque on the coil. τ onc = NAsin(θ) 14

15 WHTEOARD A 500 turn coil of wire is hinged to the top of a table. Each side of the movable coil has a length of 0.5 m. n which direction should a magnetic field point to help lift the free end of the coil off the table? Determine the torque caused by a 0.7 T field pointing in the direction described above, when there is a 0.80 A current through the wire. τ onc τ onc = NAsin(θ) = 70 Nm Summary of the differences between gravitational, electric, and magnetic forces The gravitational and electric forces exerted on objects do not depend on the direction of motion of those objects, whereas the magnetic force does. The forces exerted by the gravitational and electric fields are always in the direction of the g or E field, but the force exerted by the magnetic field on a current-carrying wire is perpendicular to both the field and the electric current. Magnetic force exerted on a single moving charged particle MAGNETC FORCE ON A CHARGED PARTCLE The magnetic field exerts a force on a current-carrying wire, which is made of moving electrons. The magnetic field also exerts a force on each individual electron. The magnetic field also exerts a force on other moving charged particles, such as protons and helium nuclei. Direction of the force that the magnetic field exerts on a moving charged particle RGHT HAND RULE #2 We can use the right-hand rule for the magnetic force to predict the direction in which electrons in the oscilloscope will be deflected. v F 2014 Pearson Education, nc. 15

16 MAGNETC FORCE ON A CHARGED PARTCLE MAGNETC FORCE ON A CHARGED PARTCLE out of the paper MAGNETC FORCE ON A CHARGED PARTCLE MAGNETC FORCE ON A CHARGED PARTCLE into the paper MAGNETC FORCE ON A CHARGED PARTCLE MAGNETC FORCE ON A CHARGED PARTCLE

Magnetic force exerted by the magnetic field on an individual charged particle The magnitude of the magnet force that the magnetic field of magnitude exerts on a particle with electric charge q

The direction of this force is determined by the right-hand rule for the magnetic force. f the particle is negatively charged, the force points opposite the direction given by the right-hand rule.

17 Magnetic force exerted by the magnetic field on an individual charged particle The magnitude of the magnet force that the magnetic field of magnitude exerts on a particle with electric charge q moving at speed v is F onq = vq sin Where is the angle between the direction of the velocity of the particle and the direction of the field. The direction of this force is determined by the right-hand rule for the magnetic force. f the particle is negatively charged, the force points opposite the direction given by the right-hand rule. WHTEOARD Each of the lettered dots shown in the figure represents a small object with an electric charge 2.0 x 10 6 C moving at a speed 3.0 x 10 7 m/s in the directions shown. Determine the magnetic force (magnitude and direction) that a 0.10-T magnetic field exerts on each object. F = 6 N (into) F = 6 N (left) F = 0 N F = 4.8 N (out) WHTEOARD WHTEOARD F = 3.2x10 13 N F = 8.64x10 16 N F = 1.728x10 13 N F = 6.4x10 22 N F c = mv2 r Circular motion in a magnetic field The force exerted by the magnetic field always points perpendicular to the particle's velocity, toward the center of the particle's path. The particle will move along a circular path in a plane perpendicular to the field. n a -field, the magnetic force exerted on a moving particle will always be perpendicular to its velocity vector. F v F F v v This means that magnetic force can never speed up a particle, and can never slow down a particle. t can only change the particle s direction! 17

W = FΔxcosθ Always 90 = 0 J A magnetic field of 0.2 T forces a proton beam of 1.5 ma to move in a circle of radius 0.1 m. The plane of the circle is perpendicular to the magnetic field.

18 Another way of saying this is WHTEOARD Magnetic force cannot do work! A -field can never add or remove kinetic energy from a system. t can only change the system s direction of motion while maintaining a constant speed. Since kinetic energy is a scalar quantity, this will leave the system s kinetic energy unchanged. W = FΔxcosθ Always 90 = 0 J A magnetic field of 0.2 T forces a proton beam of 1.5 ma to move in a circle of radius 0.1 m. The plane of the circle is perpendicular to the magnetic field. What is the speed of the proton? v = m s F C = F mv 2 = vq r v = qr m v = x x10 27 Of the following, which is the best estimate of the work done by the magnetic field on the protons during one complete orbit of the circle? (A) 0 J () J (C) 10-5 J (D) 102 J WHTEOARD (E) 1020 J v = m s Cosmic rays The auroras Cosmic rays are electrons, protons, and other elementary particles produced by various astrophysical processes, including those occurring in the Sun and sources outside the solar system. Earth's magnetic field serves as a shield against harmful cosmic rays, causing them to deflect from their original trajectory toward Earth. Charged particles moving in Earth's magnetic field follow helical paths around the magnetic field lines. 18

NTENSTY MODULATED RADATON THERAPY An MRT machine accelerates electrons to the desired kinetic energy, then uses a magnetic field to bend them into a target, resulting in the production of X-rays.

19 NTENSTY MODULATED RADATON THERAPY An MRT machine accelerates electrons to the desired kinetic energy, then uses a magnetic field to bend them into a target, resulting in the production of X-rays. Movable metal leaves then shape the X-ray beam to match the shape of the tumor. NTENSTY MODULATED RADATON THERAPY WHTEOARD Estimate the magnitude of the magnetic field needed for an MRT machine. For the estimate, assume that the electrons are moving at a speed of 2 x 10 8 m/s, the mass of the electrons is 9 x kg, and the radius of the turn is 5 cm. F C = F mv 2 = vq r = mv qr = 9x x x q A proton is launched into a uniform magnetic field Sketch the resulting path of the proton. = T The proton will take follow a circular path until it hits one of the walls of the Suppose you wanted to hook up the plates to opposite terminals of a battery, so that the proton travels straight through the plates, undeflected. q q Which way would you need to hook up the battery? (charges of the plates) 19

20 Combining electric and magnetic forces! q v E F q F q The forces will only be balanced if qv = Eq. v E f the strengths of the fields are fine-tuned so that the particle travels straight through, derive an expression for the velocity of the particle. F = vq F q = Eq Therefore, only particles with the exact velocity v = E will make it through. This device is called a velocity selector and is used in particle accelerators to hand-pick the right particles for a collision! q v E Too fast: Magnetic force too strong. Magnetic force dominates. Juuuust right! v = E What will happen if the particle is not moving fast enough? (v < E/)? What about if the particle is moving too fast? (v > E/)? Too slow: Magnetic force too weak. Electric force dominates. F = vq F q = Eq Whiteboard Challenge: Capture the Protons! m p = 1.67 x kg e = 1.6 x C eam of protons with randomly distributed speeds = 0.2 T Too fast: Magnetic force too strong. Magnetic force dominates. 2r = 20 cm E = 400 k/m a) Sketch the complete path of the protons that will make it through the velocity selector undeflected. Too slow: Magnetic force too weak. Electric force dominates. b) Where should a detector be placed along the orange wall (quantitatively) to measure the number of protons per second that made it through the velocity selector? 20

v = E The only protons that make it through the crossed E and fields must have a speed v = E v = 400,000 0.

21 v = E The only protons that make it through the crossed E and fields must have a speed v = E v = 400, v = 2x10 6 m s Magnetohydrodynamic (MHD) generator An MHD generator converts the random kinetic energy of high-temperature charged particles into electric potential energy. Once they are in the region of only -field, they will immediately move in uniform circular motion with a radius given by r = mv q r = cm And you can use RHR #2 to determine which way they will curve! MHD generators are used at some older coal-fired power plants to improve the efficiency of power generation. Magnetic flow meter A magnetic flow meter works only for fluids with moving ions, which includes most fluids. A magnetic field is oriented perpendicular to the vessel through which the fluid flows. Oppositely charged ions in the fluid are pushed by the magnetic field to opposite walls, producing a potential difference across the walls of the vessel. With this information, we can determine the fluid's volume flow rate. MAGNETC FLOW METER WHTEOARD s the general magnetic flow meter idea feasible for measuring blood speed in an artery? Estimate the potential difference you would expect to measure as blood in an artery passes through a 0.10-T magnetic field region. Assume the heart pumps 80 cm 3 of blood each second (the approximate volume for each heartbeat) and the diameter of the artery is 1.0 cm. Flow rate (chapter 11) Q = A v Electric Field (chapter 15) E = d Q = A v Q = πr 2 v Q = π d2 4 v v = 4Q πd 2 v = 4 8x10 5 π 1x10 4 v = 1.02 m s E = d v = E E = v v = d = vd = = 1.02x10 3 MASS SPECTROMETER 21

Mass Spectrometers Mass spectrometer Mass spectrometry is an analytical technique that identifies the chemical composition of a compound or sample based on the mass-to-charge ratio of charged

The ratio of charge to mass of the particles is calculated by passing them through ELECTRC and MAGNETC fields in a mass spectrometer.

t can also determine the relative concentrations of atoms of the same chemical element that have slightly different masses.

22 Mass Spectrometers Mass spectrometer Mass spectrometry is an analytical technique that identifies the chemical composition of a compound or sample based on the mass-to-charge ratio of charged particles. A sample undergoes chemical fragmentation, thereby forming charged particles (ions). The ratio of charge to mass of the particles is calculated by passing them through ELECTRC and MAGNETC fields in a mass spectrometer. A mass spectrometer helps determine the masses of ions, molecules, and even elementary particles such as protons and electrons. t can also determine the relative concentrations of atoms of the same chemical element that have slightly different masses. WHTEOARD FORCE DAGRAM - The elocity Selector When you inject the sample you want it to go STRAGHT through the plates. Since you have an electric field you also need a magnetic field to exert a force in such a way as to ALANCE OUT the electric force caused by the electric field. WHTEOARD Ratio (q/m) After leaving the velocity selector in a straight line, it enters the deflection chamber, which ONLY has a magnetic field. This field causes the ions to move in a circle separating them by mass. This is also where the charge to mass ratio can then by calculated. From that point, analyzing the data can lead to identifying unknown samples. F C = F mv 2 = vq r q m = v r MASS SPECTROMETER WHTEOARD (next slide picture) 1. Draw a force diagram (velocity selector) 2. Write an expression for the velocity v of the charged particle through the velocity selector. 3. Write an expression for the electric potential difference between plates (in terms of v, d, and ) 4. Write an expression for the of radius of the path created by the particle inside the deflection chamber. (in terms of v, m, q, and ) ELOCTY SELECTOR MASS SPECTROMETER q v p DEFLECTON CHAMER 22

WHTEOARD (Expressions for v, & r) An atom or molecule with a single electron removed is traveling at 1.0 x 10 6 m/s when it enters a mass spectrometer's 0.50-T uniform magnetic field region.

23 WHTEOARD (Expressions for v, & r) An atom or molecule with a single electron removed is traveling at 1.0 x 10 6 m/s when it enters a mass spectrometer's 0.50-T uniform magnetic field region. ts electric charge is 1.6 x C. t moves in a circle of radius 0.20 m until it hits the detector. 1. Determine the magnitude of the magnetic force that the magnetic field exerts on the ion. 2. Determine the magnitude of the Electric Field between the plates of the velocity selector. 3. Determine the mass of the ion. MASS SPECTROMETER WHTEOARD MASS SPECTROMETER WHTEOARD - solution MASS SPECTROMETER F = vq sin(θ) F = 8x10 14 N E = v E = 5x10 5 m q F C = F m = qr sin(θ) v m = 1.6x1 26 kg MASS SPECTROMETER MASS SPECTROMETER q q 23

24 MASS SPECTROMETER q 24

Magnetic Fields and Forces

Nicholas J. Giordano www.cengage.com/physics/giordano Chapter 20 Magnetic Fields and Forces Marilyn Akins, PhD Broome Community College Magnetism Magnetic fields are produced by moving electric charges