Magnetism Physics 122 11/10/2018 Lecture XII

Magnetic force on moving charge Magnetic force F is perpendicular to the velocity v of a particle with charge q F=qvB sin q Magnetic field does not change the magnitude of particle’s velocity, only its direction. Charged particles move in circles in constant magnetic field 11/10/2018 Lecture XII

Magnetic force on moving charge Circular motion Magnetic force = Centripetal force F=qvB Centripetal acceleration a=v2/R Newton’s second law F=ma qvB=mv2/R In experiments B is known, q=e most of the time, Measure R- measure mv For a given v measure m – magnetic spectrometer 11/10/2018 Lecture XII

Cyclotron frequency Frequency does not depend on v! For a given particle type (q,m=const) it depends only on B 11/10/2018 Lecture XII

Particle selector + Crossed E and B fields: For one given velocity electric force exactly compensates magnetic force Only particles with this value of velocity emerge from particle selector + + + + - - - - + 11/10/2018 Lecture XII

Crossed fields Electric field changes kinetic energy of charged particle qDV=mv2/2 Magnetic field does not change KE, only direction Lorentz force: 11/10/2018 Lecture XII

Torque 11/10/2018 Lecture XII

Current loop in magnetic field A=ab – area of the loop Magnetic field exerts a torque on a loop parallel to the magnetic field: 11/10/2018 Lecture XII

Current loop in magnetic field q – angle between magnetic field and a perpendicular to the loop !!! Magnetic field orients a loop current perpendicular to B. N loops: 11/10/2018 Lecture XII

Magnetic moment Current loop (area A, current I, number of turns N) in constant magnetic field B experiences torque Define magnetic moment m perpendicular to the plane of the loop Torque 11/10/2018 Lecture XII

Magnetic moment Equilibrium position for current loop is when B is perpendicular to the face of the loop, or when magnetic moment is parallel to B Inside magnetic field magnetic moments orient parallel to the field Galvanometer: B is know – measure I 11/10/2018 Lecture XII

Magnetic field created by currents Electric currents – moving electric charges - create magnetic field Stationary electric charges do not create magnetic filed First right hand rule Thumb along the current Wrap your fingers around the wire fingers show the direction of the magnetic field 11/10/2018 Lecture XII

Magnetic field created by current Magnetic field B created by current I at a distance r from the conductor is m0 = 4p 10-7 Tm/A- magnetic permeability of free space 11/10/2018 Lecture XII

Ampere’s Law In a way similar to Gauss’s law for E and Q Not flux, integral over closed path Only component of B parallel to dl contributes to integral 11/10/2018 Lecture XII

Application of Ampere’s Law Thick wire of radius R carries current I. What is B(r ) in and outside of the wire? Current through unit area: Current through circle radius r<R Path integral over radius r Ampere’s law For r>R – same as thin wire 11/10/2018 Lecture XII

Practical application: coaxial cable Cylindrical braid carries return current  magnetic field outside is zero. 11/10/2018 Lecture XII