Physics 202, Lecture 11 Today s Topics Exam 1 Result Magnetic ields and orces (Ch. 29) Magnetic materials Magnetic forces on moving point charges Magnetic forces on currents, current loops Motion of charge in uniform field Thurs: applications (cyclotron, velocity selector, Hall effect) Homework #5: due 10/15,10 PM Optional reading quiz: due 10/12, 5 PM Exam 1 Results Median: 57 Average: 57.3 Std dev: 15.3 Grade ranges (approx): 75-96 A 68-74 A 57-67 48-56 C 37-47 C <37 D 1
Magnetism: Overview Previously: electrostatics orces and fields due to stationary charges Coulomb force E, Electrostatic field E: E = q E Now: magnetism (historically: magnetic materials, Oersted effect) orces and field due to moving charges (currents) Magnetic orce, magnetic field : = qv = d l " (charges: Lorentz force) (currents: iot-savart law) Magnetic Materials (1) ocus first on bar magnets (permanent magnets): Two types of poles: N and S Magnetic forces: like poles repel, opposite poles attract Magnetic field: (vector field). Units: 1 Tesla (T) = 1 N/(A m) Direction: as indicated by compass s north pole ield lines: Outside magnet: N to S nside magnet: S to N 2
Typical Magnetic ield Strengths 1 Gauss = 10-4 Tesla Electrostatics analogy: Electric ield Lines of an Electric Dipole dipole field Magnetic ield Lines of a bar magnet 3
Magnetic Monopoles Perhaps there exist magnetic charges, just like electric charges: magnetic monopole (+ or - magnetic charge). How can you isolate this magnetic charge? Try cutting a bar magnet in half: S N S N S N Even an individual electron has a magnetic dipole Despite extensive searches, magnetic monopoles have never been found id A = 0 " (compare Gauss s Law) ar Magnets and Compass Recap: 2 magnetic poles, N and S like poles repel, opposite poles attract both poles attract iron (ferromagnetic material) Two poles not separable Compass: a bar magnet ts north pole (conventionally defined) points towards the northern direction N S S Magnets Modern compasses An ancient Chinese compass (~220C) 4
South Magnetic Pole Earth s Magnetic ield Geographic North Pole N S Magnetic orce We know about the existence of magnetic fields by the force they exert on moving charges. What is the "magnetic force"? How is it distinguished from the "electric" force? Experimental observations about the magnetic force : a) magnitude: to velocity of q q v b) direction: to direction of q s velocity c) direction: to direction of is the magnetic field vector 5
Magnetic orce orce on charge q moving with velocity v through region of space with magnetic field : v q = q v v q f also electric field E: Lorentz = q E orce + q v Law v q = 0 = q v Cross product review (board; see also text Ch 11.1): direction: right hand rule magnitude: = qvsin v θ +q 6
Exercise: Direction of Magnetic orce ndicate the direction of in the following situations: +q v v -q Question 1 : Direction of Magnetic orce Which fig has the correct direction of? -q -q -q -q 7
Question 2 : Direction of Magnetic orce Which fig has the correct direction of? +q +q +q +q Magnetic orce On Current Carrying Wire(1) Now you know how a single charged particle moves in a magnetic field. What about a group? n a portion of current-carrying conducting wire: n A number of charges per unit volume area of the conductor dl length of the element v d drift velocity of a charge then = nadl q v d ( ) = d l A dl n v d " # d l = L (for uniform field) 8
Magnetic orce On A Current Carrying Wire (2) Top View Also: bending electron beam Magnetic orce On Current Carrying Wire(3) or a uniform magnetic field: To get the sum of a number of vectors - put them all head to tail and connect the initial (a) and final point (b): b d l = L ba a b a f the initial and final points are the same, the integral is zero There is no net magnetic force on a closed current loop in a uniform magnetic field. 9
orces on a Current Loop or current loops in a uniform magnetic field as shown, what is the direction of the force on each side? =0.................... X 4 1 3 =0 2............ 1........ 4................................................ 3................................ 2 Case 1 recall:σ =0 Case 2 Torque on Current Loop in Uniform ield Though the net magnetic force on a closed current loop in a uniform field is zero, there can be a net torque. Case 1: A θ=π/2 X Loop has length dimension a (normal to ), width b. = 2 b sin" = absin" 2 = A " Define the magnetic moment µ # A = µ " More general: A θ X µ = N A (N turns) 10
Magnetic Dipole Moments Magnetic dipole moment µ. S N µ Macroscopic µ=a Microscopic µ L angular momentum of orbiting or spin definition of magnetic moment = 0 " = " µ # U = - µi µ in ield Trajectory in Constant ield (1) Suppose charge q enters a uniform -field with velocity v. What will be the path that q follows? v x x x x x vx q orce perpendicular to velocity: uniform circular motion Note: magnetic force does no work on the charge Kinetic energy constant R 11
Trajectory in Constant ield (2) orce: = qv centripetal acc: a = v2 R Newton's 2nd Law: v x x x x x vx q R = ma qv = m v2 R = mv q = p q R Cyclotron frequency: = v R = q m 12