Recitation 9 P H Y S 2 4 1 OCTOBER 17, 2013 Clicker Question 1 Two wires carrying current i experience a no net force due to an external magnetic field. What can you say about the current in the two-wire system? A) Currents are parallel B i dl B) Currents are anti-parallel z C) Impossible to determine y x FB idl B A current i runs through a rectangular loop of wire. The wire is exposed to a uniform magnetic field. Find the net force on the wire. B F i w B z z back idl y y d Fright Fleft 0 x x F i w B w front Outline Biot-Savart Maxwell’s equations Law of Biot-Savart FB idl B idl rˆ B 0 4 r 2 T m2 4 107 0 A Group Clicker Question A wire carries current into the page. What direction is the magnetic field around the wire? A) Clockwise idl B) Counter-clockwise C) Radially outward D) Radially inward E) None of the above Group Clicker Question A wire carries current into the page. What direction is the magnetic field around the wire? idl rˆ B Group Clicker Question A wire carries current into the page. What direction is the magnetic field around the wire? idl rˆ B Group Clicker Question A wire carries current into the page. What direction is the magnetic field around the wire? idl rˆ B Right Hand Rule Shortcut for determining the Magnetic field: 1. Grab the current with your thumb pointing the direction of the flow 2. Fingers give the direction of the magnetic field http://basic-electronics.com/vector3dm/ Group Question: Group Clicker Question Five particles have the same magnitude pA pB of the momentum. Rank the particles according to their angular momentum about ‘X’. pC pD pE Group Clicker Question p Five particles have the same magnitude A of the momentum. Rank the particles according to their angular momentum about ‘X’. rA rA, θ l r p r A,|| l p r sin l p r l p r Group Clicker Question Five particles have the same magnitude pA pB of the momentum. Rank the particles according to their angular momentum about ‘X’. r r r r r p A, B, D, E, C, p C D lA lB lD lE lC pE Magnetic field from a wire z idl 1) Determine the direction of the magnetic field (R-H-R) R 2) Find an expression for r-hat 3) Integrate y x (do on board) Magnetic field from a wire l 0 idl rˆ B 2 z 4 0 r idl l i dl r sin 0 ˆ B 3 i 4 0 r R l i dl r 0 ˆ B 3 i 4 0 r y iR l dx x 0 ˆ B 3 i 4 0 R 2 x 2 2 Magnetic field from a wire iR l dx 0 ˆ B 3 i 4 0 R 2 x2 2 z idl iR x l B 0 | 2 2 2 1 2 4 R R x 0 R i l B 0 2 2 1 2 4 RR l y x Outline Biot-Savart Maxwell’s equations Maxwell’s equations Electric field Magnetic field Gauss’s Law for qenc E dA electric field 0 Gauss’s Law (electric field) E Q Maxwell’s equations Electric field Magnetic field Gauss’s Law for qenc Gauss’s law E dA B dA 0 electric field for magnetism 0 E Gauss’s Law (for magnetism) B dA 0 B N S Maxwell’s equations Electric field Magnetic field Gauss’s Law for qenc Gauss’s law E dA B dA 0 electric field for magnetism 0 E B d Maxwell-Ampere B dl i E 0 enc 0 0 dt law Maxwell-Ampere Law d B dl i E 0 enc 0 0 dt Ampere’s law Maxwell’s correction Ampere’s Law B dl 0ienc B Maxwell’s equations Electric field Magnetic field Gauss’s Law for qenc Gauss’s law E dA B dA 0 electric field for magnetism 0 E B d Maxwell-Ampere B dl i E 0 enc 0 0 dt law B Maxwell’s equations Electric field Magnetic field Gauss’s Law for qenc Gauss’s law E dA B dA 0 electric field for magnetism 0 E B Faraday’s Law d Maxwell-Ampere B dl i E of induction 0 enc 0 0 dt law B Maxwell’s equations Electric field Magnetic field Gauss’s Law for qenc Gauss’s law E dA B dA 0 electric field for magnetism 0 E B Faraday’s Law d d Maxwell-Ampere E dl B B dl i E of induction dt 0 enc 0 0 dt law E B James Maxwell from the Mechanical Universe (good visualization of Maxwell’s equation) https://www.youtube.com/watch?v=VdoL8IOwJw0 The story of Electricity (BBC) https://www.youtube.com/watch?v=uhgo9fAlAQQ (Ep. 1) https://www.youtube.com/watch?v=NtNdQ2UOG_0 (Ep. 2) https://www.youtube.com/watch?v=MT8yeMzHvKY (Ep. 3) Maxwell’s equations (differential form) Electric field Magnetic field Gauss’s Law for E enc B 0 Gauss’s law for magnetism electric field 0 Faraday’s Law dB E B i Maxwell’s law of induction dt 0 enc.