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Chapter 20 Magnetism 20.1 Magnets and Magnetic Fields Magnets have two ends – poles – called north and south. Like poles repel; unlike poles attract. 20.1 Magnets and Magnetic Fields However, if you cut a magnet in half, you don’t get a north pole and a south pole – you get two smaller magnets. Ferromagnetism • Ferromagnetism is the basic mechanism by which certain materials (such as iron) form permanent magnets, or are attracted to magnets. • The spin of an electron, creates a small magnetic field. Electrons have either “up” or “down” spins and are often paired up with down. Atoms with unpaired electron spins can have a net magnetic effect. • Iron, Nickel, Cobalt and their alloys are most notable ferromagnetic materials Ferromagnetism: Domains When the material is unmagnetized, the domains are randomly oriented. They can be partially or fully aligned by placing the material in a strong external magnetic field. Domains are formed by small regions where atoms are aligned such that their individual electron spins are in the same direction. 20.1 Magnets and Magnetic Fields Magnets cause space to be modified in their vicinity, forming a “magnetic field”. The magnetic field caused by magnetic “poles” is analogous to the electric field caused by electric “poles” or “charges”. Magnetic field lines differ from electric field lines in that they are continuous loops with no beginning or end. 20.1 Magnets and Magnetic Fields The Earth’s magnetic field is similar to that of a bar magnet. Note that the Earth’s “North Pole” is really a south magnetic pole, as the north ends of magnets are attracted to it. Units of Magnetic Field Tesla (SI) – N/(C m/s) – N/(A m) Gauss – 1 Tesla = 104 gauss Magnetic Force on Particles Magnetic fields cause the existence of magnetic forces. A magnetic force is exerted on a particle within a magnetic field only if – the particle has a charge. – the charged particle is moving with at least a portion of its velocity perpendicular to the magnetic field. Magnetic Force on a Charged Particle (Lorentz Force) • magnitude: F = qvBsinθ – q: charge in Coulombs – v: speed in meters/second – B: magnetic field in Tesla – θ: angle between v and B • direction: Right Hand Rule • FB = q v x B (This is a “vector cross product”) Magnetism Magnetic force (Lorentz force) Magnetic Force Sample Problem: Calculate the magnitude and direction of the force exerted on a 3.0 μC charge moving north at 300,000 m/s in a magnetic field of 200 mT if the field is directed a) North. b) South. c) East. d) West. Magnetic forces… • are always orthogonal (at right angles) to the plane established by the velocity and magnetic field vectors. • can accelerate charged particles by changing their direction. • can cause charged particles to move in circular or helical paths. Magnetic forces cannot... • change the speed or kinetic energy of • charged particles do work on charged particles. Magnetic Forces… …are centripetal. • Remember that centripetal acceleration is v2/r. • Remember centripetal force is therefore mv2/r. 20.4 Force on Electric Charge Moving in a Magnetic Field If a charged particle is moving perpendicular to a uniform magnetic field, its path will be a circle. Motion of Charged Particles in a Magnetic Field Case 1: Velocity perpendicular to magnetic field Movement of charged particles in B Field http://wps.aw.com/aw_young_physics_11/13 /3510/898593.cw/index.html http://video.mit.edu/watch/cloud-chamber-4058/ Sample Problem: An electric field of 2000 N/C is directed to the south. A proton is traveling at 300,000 m/s to the west. What is the magnitude and direction of the force on the proton? Describe the path of the proton? Ignore gravitational effects. Sample Problem: A magnetic field of 2000 mT is directed to the south. A proton is traveling at 300,000 m/s to the west. What is the magnitude and direction of the force on the proton? Describe the path of the proton? Ignore gravitational effects. Sample Problem: How would you arrange a magnetic field and an electric field so that a charged particle of velocity v would pass straight through without deflection? Motion of Charged Particles in a Magnetic Field Velocity selector Mass Spectrometer Motion of Charged Particles in a Magnetic Field Mass spectrometer Motion of Charged Particles in a Magnetic Field Mass spectrometer Force on an Electric Current in a Magnetic Field A magnet exerts a force on a current-carrying wire. The direction of the force is given by the right-hand rule. Video: wire in B field Fingers: direction of conv. current, I Curl fingers: dir. of magnetic field, B thumb: direction of force, F Magnetic Force on a Current-Carrying Conductor Magnetic force on a current (in a straight wire) Sample Problem: What is the force on a 100 m long wire bearing a 30 A current flowing north if the wire is in a downwarddirected magnetic field of 400 mT? After ½ turn: To summarize: Magnetic Fields… Affect moving charge – F = qvBsinθ – F = ILBsinθ – Right Hand Rule is used to determine direction of this force. Magnetic fields are also caused by moving charge… Electric Currents Produce Magnetic Fields Experiment shows that an electric current produces a magnetic field. When brought into the field, a magnet will experience a force due to the current, in the same way as iron filings close by a bar magnet experience a force causing them to align to the magnetic field. Magnetic fields produced by straight currents: Magnitude of Magnetic Field produced by straight currents μo: 4π × 10-7 T m / A (called magnetic permeability of free space) I: current (A) r: radial distance from center of wire (m) Sample Problem: What is the magnitude and direction of the magnetic field at point P, which is 3.0 m away from a wire bearing a 13.0 Amp current? Sample problem: what is the magnitude and direction of the force exerted on a 100 m long wire that passes through point P which bears a current of 50 amps in the same direction? 20.6 Force between Two Parallel Wires The magnetic field produced at the position of wire 2 due to the current in wire 1 is: The force this field exerts on a length l2 of wire 2 is: (20-7) 20.6 Force between Two Parallel Wires Parallel currents attract; antiparallel currents repel. Principle of Superposition When there are two or more currents forming a magnetic field, calculate B due to each current separately and then add them together using vector addition. Sample Problem: What is the magnitude and direction of the electric field at point P if there are two wires producing a magnetic field at this point? Sample Problem: Where would the magnetic field be zero? Solenoid • A solenoid is a coil of wire. • When current runs through the wire, it causes the coil to become an “electromagnet”. • Air-core solenoids have nothing inside of them. • Iron-core solenoids are filled with iron to intensify the magnetic field. Electric Currents Produce Magnetic Fields RHR for direction of field Thumb: direction of current Fingers then wrap in direction of field magnetic field reversal A geomagnetic reversal is a change in the Earth’s magnetic field such that the positions of magnetic north and magnetic south are interchanged. The Earth’s field has alternated polarity, with the time spans of reversal randomly distributed; most being between 0.1 and 1 million years with an average of 450,000 years. Most reversals are estimated to take between 1,000 and 10,000 years. The latest one, occurred 780,000 years ago. Earth’s Magnetosphere A magnetosphere is formed when a stream of charged particles, such as the solar wind, interacts with and is deflected by the magnetic field of a planet or similar body solar corona aurora borealis An aurora is a natural light display in the sky particularly in the arctic and antarctic regions, caused by the collision of charged particles with atoms in the upper atmosphere. The charged particles originate in the magnetosphere and, on Earth, are directed by the Earth’s Magnetic Field into the atmosphere. The key ingredient in anything magnetic is 1. 2. 3. the surrounding magnetic field pairs of magnetic poles moving electric charge 0% 1 0% 2 0% 3 Every spinning electron is a tiny magnet. Since all atoms have spinning electrons, why are not all atoms tiny magnets? 1. 2. 3. Because the magnetic field cancels out in most atoms Because the electrons don’t spin fast enough They don’t align properly 0% 1 0% 2 0% 3 What is so special about iron that makes each iron atom a tiny magnet? 1. 2. 3. It is a metal It has unpaired electrons It has more electrons than protons 0% 1 0% 2 0% 3 A magnetic field can be found surrounding any 1. 2. 3. 4. Moving electric charge Current carrying wire Neither of these Both of these 0% 1 0% 0% 2 3 0% 4