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Chapter 27 – Introduction to Magnetic Fields – Review – Electric Fields 1. A charge (or charges) produce an Electric Field in the space around it. 2. Another charge responds to this field (experiences a force) What is coming up for Magnetic Fields 1. A MOVING charge (or charges) produce an Magnetic Field in the space around it. 2. Another MOVING charge responds to this field (experiences a force) Some Simple Phenomenology – First Guess – Magnetic Forces are just like Electric Forces Just Replace + & - with N & S This is an extremely good idea that is, unfortunately WRONG The Basic Problem is that there are no “Free” N & S poles. Experiments show that there is a fundamental relationship between Magnetic Fields and Electric Currents Oersted’s Experiment Place a compass near a wire Compass deflects when an electric current flows in the wire N Motion of a charged particle in a Magnetic Field 1. A moving charge or a electric current produces a magnetic field in the surrounding space (It also produces an electric field) 2. The magnetic field exerts a force on any other moving charge or current that is in the field. Strategy: We will begin with a discussion of the force on a moving charge (part 2.) Then we will discuss how a moving charge makes the field (part 1.) Some examples of the force on a moving charge in a magnetic field observation #1- The magnetic force is always perpendicular to the magnetic field observation #2- The magnetic force is always perpendicular to the particle velocity The “Vector” or “Cross Product” v r r If C = A × B then the magnitude r of where θ is the angle between A and is given by the “Right Hand Rule”: r r v C r = A B sin θ , r B . The direction of C Advice on using the Right Hand Rule: 1) First determine the plane that contains A and B. The cross product will point perpendicular to that plane. There are only two choices. 2) Use the Right Hand r Ruler to rpick which choice is correct. 3) If you are using F = qv × B , Remember that a negative charge will reverse the direction of the cross product! r r r F = qv × B F = q vB⊥ Units of Magnetic Field: 1 Tesla = 1 T = 1 Newton/(Ampere·meter) Motion of Charged Particles in Magnetic and Electric Fields r r r v F = q( E + v × B ) EM force – “Lorentz” Force + v r d2 r F = ma = m 2 r dt Newton’s 2nd Law r r d r r r d2 r q[ E ( r ) + r × B( r )] = m 2 r dt dt r r (t ) Differential equation Solution = “Equation of Motion” For constant force there are two important simple cases: v r r r r Uniform linear acceleration v = v0 + at F is parallel to v v r F is perpendicular to v Uniform circular motion Uniform Circular Motion (see Y & F Chapter 3) Similar triangles gives Average acceleration r ∆v ∆s = v1 R r v1 ∆v = ∆s R r ∆v v1 ∆s = R ∆t ∆t r ∆v v1 r ∆s a = lim ∆t →0 = lim ∆t →0 R ∆t ∆t r v2 a = R Uniform Circular Motion implies a acceleration that is always directed towards the center of the circle. r Amplitude of acceleration is constant: r mv 2 F = ma = R Direction of acceleration changes with time Angular Velocity (see Y& F chapter 9) Uniform Circular Motion is described by an “Angular Velocity” ds Since s = rθ and v = dt v = rω v2 a= = rω 2 r v2 F = m = mrω 2 r ω≡ Angular Velocity (radians/s) Frequency ω f = 2π cycles/s=Hertz Period 1 T= f seconds dθ ω= dt Angular Velocity as a vector (see Y& F chapter 9) ┴ Right Hand Rule Gives Sense of Rotation Given by Torque End of Chapter 27 You are responsible for the material covered in T&F Sections 27.1 -27.8 You are expected to: • Understand the following terms: magnetic field, magnetic force, uniform circular motion, angular velocity, angular acceleration, torque, magnetic dipole moment • Be able to calculate the force on a moving charge in a uniform magnetic field, be able to calculate the force on a current carrying conductor, be able to calculate the torque on a loop of wire. Recommended F&Y Exercises chapter 27: 33,39,41,45