3­Magnetism.notebook May 08, 2014 Unit 9­Magnetism This end points to the North; call it "NORTH." This end points to the South; call it "SOUTH." 1 3­Magnetism.notebook May 08, 2014 The behavior of magnetic poles is similar to that of like and unlike electric charges. Law of Magnetic Poles like poles repel, and unlike poles attract 2 3­Magnetism.notebook May 08, 2014 Magnetic Field (B) altered region in space around a magnet where the magnet's influence can be felt The direction of the magnetic field at any point in space is the direction indicated by the north pole of a small compass needle placed at that point. http://phet.colorado.edu/en/simulation/magnet­and­compass 3 3­Magnetism.notebook May 08, 2014 The magnetic field lines and pattern of iron filings in the vicinity of a bar magnet and the magnetic field lines in the gap of a horseshoe magnet. 4 3­Magnetism.notebook May 08, 2014 What about atoms makes them magnets? Unpaired electrons both orbit and spin, producing a mini­magnet in each atom. Most materials have random alignment of these atoms, but ferromagnetic materials get "huge" (0.01­0.1 mm across chunks (called magnetic domains) all aligned with each other. Induced magnetism comes about for two reasons: 1. domains close to the orientation of the external magnetic field grow in size at the expense of the other domains. 2. some domains rotate and become more oriented in the direction of the magnetic field. 5 3­Magnetism.notebook May 08, 2014 The magnetism induced in a ferromagnetic material can be very large, even with a weak external magnetic field. 6 3­Magnetism.notebook May 08, 2014 Magnetic Fields and Moving Charges Charges in electric fields experience electric forces. Charges in magnetic fields MIGHT experience magnetic forces. 1. The charge must be moving. 2. The velocity of the moving charge must have a component perpendicular to the direction of the magnetic field. No Fm Maximum Fm Fm < Maximum 7 3­Magnetism.notebook May 08, 2014 Strength of the Magnetic Field and Force B = Fm |q0| v sin θ Fm = Magnetic Force q0 = Charge v = Charge's Velocity B = Magnetic Field Fm = q0 v x B Units: N s = 1 Tesla (T) C m Nicola Tesla Croatian­American 1856­1943 1 gauss = 10­4 Tesla 8 3­Magnetism.notebook May 08, 2014 Direction of the magnetic force Right hand rule #1 for magnetism: 1. Right thumb points in the direction of the velocity. 2. Right fingers point in the direction of the magnetic field. 3. Right palm pushes in the direction of the magnetic force. 9 3­Magnetism.notebook May 08, 2014 10 3­Magnetism.notebook May 08, 2014 11 3­Magnetism.notebook May 08, 2014 The Motion of a Charged Particle in a Magnetic Field Charged particle in an electric field. The electrical force can do work on a charged particle. Charged particle in a magnetic field. The magnetic force cannot do work on a charged particle. 12 3­Magnetism.notebook May 08, 2014 The magnetic force always remains perpendicular to the velocity and is directed toward the center of the circular path. 13 3­Magnetism.notebook May 08, 2014 14 3­Magnetism.notebook May 08, 2014 15 3­Magnetism.notebook May 08, 2014 The Mass Spectrometer • identifies unknown molecules in chemical reactions • give anesthesiologists information on the gasses in the patient's lungs (for a singly ionized particle starting from rest) Substituting equation 2 into equation 1 for velocity: 16 3­Magnetism.notebook May 08, 2014 17 3­Magnetism.notebook May 08, 2014 The Force on a Current in a Magnetic Field The magnetic force on the moving charges pushes the wire to the right. 18 3­Magnetism.notebook May 08, 2014 Calculating the Force on a Current in a Magnetic Field FB = qv x B Multiply right side by t / t. FB = q tv x B t Simplify: FB = l I x B 19 3­Magnetism.notebook May 08, 2014 20 3­Magnetism.notebook May 08, 2014 What are the top and bottom forces producing? 21 3­Magnetism.notebook May 08, 2014 The Torque on a Current­Carrying Coil The two forces on the loop have equal magnitude but an application of RHR­1 shows that they are opposite in direction. 22 3­Magnetism.notebook May 08, 2014 The Torque on a Current­Carrying Coil The loop tends to rotate such that its normal becomes aligned with the magnetic field. 23 3­Magnetism.notebook May 08, 2014 Calculating the Torque on a Current­Carrying Coil N = number of coils NIA = magnetic moment (in A m2) 24 3­Magnetism.notebook May 08, 2014 25 3­Magnetism.notebook May 08, 2014 26 3­Magnetism.notebook May 08, 2014 Magnetic Fields Produced by Currents A current carrying wire experiences a magnetic force when it is in a magnetic field. But, a current carrying wire also produces a magnetic field of its own! 27 3­Magnetism.notebook May 08, 2014 Magnetic Fields Produced by Currents Right­Hand Rule No. 2. Curl the fingers of the right hand into the shape of a half­circle. Point the thumb in the direction of the conventional current, and the tips of the fingers will point in the direction of the magnetic field. 28 3­Magnetism.notebook May 08, 2014 Magnetic Fields Produced by Currents A LONG, STRAIGHT WIRE From experiments: I B α r μ0 = Permeability of Free Space = 4π x 10-7 T m/A 29 3­Magnetism.notebook May 08, 2014 Magnetic Fields Produced by Currents 30 3­Magnetism.notebook May 08, 2014 31 3­Magnetism.notebook May 08, 2014 Magnetic Fields Produced by Currents MAGNETIC FIELD PRODUCED BY A LOOP OF WIRE If you have multiple (N) loops: μ0 I B = N 2R 32 3­Magnetism.notebook May 08, 2014 53. A long solenoid has 1400 turns per meter of length, and it carries a current of 3.5 A small circular coil of wire is placed inside the solenoid with the normal to the coil oriented at an angle of with respect to the axis of the solenoid. The coil consists of 50 turns, has an area of 1.2 x 10­3 m2, and carries a current of 0.50 A. Find the torque exerted on the coil. 33 3­Magnetism.notebook May 08, 2014 56. Two long, straight wires are separated by 0.120 m. The wires carry currents of 8.0 A in opposite directions, as the drawing indicates. Find the magnitude of the net magnetic field at the points labeled A and B. 34 3­Magnetism.notebook May 08, 2014 Ampère’s Law • Ampère found a procedure for deriving the relationship between the current in an arbitrarily shaped wire and the magnetic field produced by the wire. • Ampère’s Circuital Law • ΣB|| Δℓ = µo I • Sum over the closed path André‐Marie Ampère 1775 – 1836 French 35 3­Magnetism.notebook May 08, 2014 Ampère’s Law ΣB|| Δℓ = µo I B|| ΣΔℓ = µo I factoring out B since it is the same for all elements B|| ΣΔℓ = µo I distance around the shape For a circle: B is always perpendicular to radius (parallel to tangent) B|| = B B Σ Δ l = μ0 I B (2πr) = μ0 I B = μ0 I 2πr 36 3­Magnetism.notebook May 08, 2014 37