Magnetic Fields

Physics 202, Lecture 12 12 Today?s Topics ? Magnetic Field (Ch 29, part II) ? Force on Current Carrying Wires Wires ? For and Torque on a Current Loop In Uniform B Field ? Magnetic dipoles ? Motion of a Charged Particle In a Uniform B Field ? Applications: MtiCfi t ? Magnetic onfinemen ? First Modern Particle Accelerator: Cyclotron ? Mass Selector (q/m) ? Hall Effect. Magnetic Force On Current Carrying Wire Segment (Review of Last Lecture)g( ? Magnetic force on a current segment of length L in uniform field B: F ? B IL B B = qvx = x ? Key steps to derive: ? Current: moving charges I= qnv A moving charges. d ? Magnetic force on charge q: qv d xB ? F B =qv d xB (ALn) =ILxB() Demo: Magnetic Force On A Current Carrying Wiregy Top View Vi Also demo: Bending electron beam Magnetic Force On Current Carrying Wire ? Magnetic force on a curved wire in uniform field B : F B =IL?xB ? Derivation: See board Note:Net force on a current loop in uniform B field is zero L? I B ds Review Exercise: Forces On A Current Loop ? For a current loop in a uniform magnetic field as shown, what is the direction of the force on each side? (Lecture 11 review: F B = ILxB ) F 0 F B I 1 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I 1 4 B = II 2 B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II 2 X ? F B F B I 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I 3 F B =0 F B Case 1 Case 2 recall:?F B =0 Torque on a Current Loop In Uniform B Field ? Exercise: For a current loop in a uniform B field, show that the torque on the loop is: |?|=IABsin? (Quiz: In what direction?) ?Conveniently, the result can be rewritten as: BA rr r ×= I? B 1 I I I 4 a F 4 A ? ? IA: magnetic dipole moment I 2 3 x B bsin? b F 2 face view top view A : Area Vector Magnetic Dipole Moments N ? Magnetic dipole moment ?. B ? S F= ? r 0 Macroscopic ?=IA B-U B ?= ×= ? ?? r v Microscopic ?? L angular momentum of orbiting or spin iBFild? in B Field definition of magnetic moment Review and Compare: Electric Dipole Moments Dipole Moments ? Electric dipole moment p. + +q - p= qd -q ? 0 E F= r EU p×=? -p?= Review of Chapter 8: Stable and Unstable Equilibrium B ? B ? F B = 0 ? B = 0 F B = 0 ? B = 0 U= -?B (low) (d 2 U/d? 2 >0) U= +?B (high) (d 2 U/d? 2 <0) ? Stable Equilibrium ? Unstable Equilibrium The picture is also true for electric dipole momentpp E p E p stable unstable Quick Quiz 1 ? A magnetic dipole moment initially points at 45 o . When a uniform horizontal B field is applied, which f th f ll i ill h ? ? o the o ow ngs w appen 1 No change B ? . 2. Points towards the B field ? B ? 3. Points against the B field B ? 4. Points normal to the B field B? Quick Quiz 2 ? A magnetic dipole moment initially points at 135 o . When a uniform horizontal B field is applied, which f th f ll i ill h ? ? o the o ow ngs w appen 1 No change B ? . 2. Points towards the B field ? B ? 3. Points against the B field B ? 4. Points normal to the B field B? Motion Of Charged Particle in a Uniform B Field ? Exercise: Show that if a charged particle q of mass m in a uniform B field has an initial velocity v in the ldiltBittiifplane perpendicu ar o , its motion is a uniform circular motion in that plane with ? radius r= mv/qB ? period: T= 2?r/v = 2?m/qB ?Note: T is independent of v Solution: see board. (recall: uniform circular motion) Motion Of Charged Particle in a Uniform B Field ?General 3D Case ?On the plane perpendicular to B: /B?r=mv ? /qB ?T= 2?m/qB ?Parallel to B spacing between helix d = v // T= v // 2?m/qB Application: Magnetic Confinement Magnetic Bottle Van Allen Belts Tokamak MST: Madison Symmetric Torus Application: Cyclotron (First Modern Particle Accelerator)() ? Explain how a cyclotron works (see board) Fixed Frequency First Cyclotron (1934) Lawrence & Livinston Application: Mass Selector ? Explain how a mass selector work (next week?s lab) speed selected: v=E/B Velocity Selector Mass selected: m/q=rB 0 /v =rB 0 /(E/B) Mass Selector Mass Selector: J.J Thomson Apparatus (1897) () ? This is your lab next week: measuring e/m Application: The Hall Effect ? Explain how Hall Effect works nqt IB V H =? See demo Yibin Pan Microsoft PowerPoint - phy202_lect12_pre.ppt [Compatibility Mode]