Exam 2 is Tuesday Oct. 27 5:30-7 pm, Birge 145 Students w / scheduled academic conflict please stay after class TODAY to arrange alternate time. Covers: all material since exam 2 Book sections: Chap 27, 29, 30 (not 30.7), 31, 32 33.1-4, 33.7-8 Bring: Calculator One (double-sided) 8 1/2 x 11 note sheet Exam review: Thursday, Oct. 22, in class Tue. Oct. 20, 2009 Physics 208 Lecture 14

Last time… RC circuits Magnetic fields Magnetic forces Tue. Oct. 20, 2009 Physics 208 Lecture 14

Magnetic force on electric charges Effect of uniform B-field on charged particle Charged particle not moving no effect Charged particle is moving: Force is perpendicular to Magnetic Field Particle Velocity Depends on sign of charge Tue. Oct. 20, 2009 Physics 208 Lecture 14

Magnetic force on charged particle Magnitude of force is proportional to Charge of particle, q Speed of particle, v Strength of magnet field, B sin(), =angle between and Direction of force is perpendicular to both and vector ‘cross product’ Tue. Oct. 20, 2009 Physics 208 Lecture 14

FB on a Charge Moving in a Magnetic Field, Formula FB = q v x B FB is the magnetic force q is the charge v is the velocity of the moving charge B is the magnetic field SI unit of magnetic field: tesla (T) CGS unit: gauss (G): 1 T = 104 G (Earth surface 0.5 G) Tue. Oct. 20, 2009 Physics 208 Lecture 14

Quick Quiz The three charges below have equal charge and speed, but are traveling in different directions in a uniform magnetic field. Which particle experiences the greatest magnetic force? B 1 2 3 1 2 3 All same F = q v B sin(q) Tue. Oct. 20, 2009 Physics 208 Lecture 14

Quick Quiz The three charges below have equal charge and speed, but are traveling in different directions in a uniform magnetic field. The force on all the particles is in the same direction. B 1 2 3 True False All forces are into page Magnitude F = q v B sin(q) Tue. Oct. 20, 2009 Physics 208 Lecture 14

Force on moving charged particle intermediate Tue. Oct. 20, 2009 Physics 208 Lecture 14

Field direction notation Field direction indicated by vector In-plane : draw vector Not in-plane : into-page out-of-page Tue. Oct. 20, 2009 Physics 208 Lecture 14

More force examples Force from B-field on moving charged particle x x x x x x v B q ® ® ® ® ® v B q ­ ­ ­ ­ ­ ­ ­ ­ v B q F ´ F F = 0 Units: 1 T (tesla) = 1 N / Am 1G (gauss) = 10-4 T Tue. Oct. 20, 2009 Physics 208 Lecture 14

Magnetic Force on a Current Force on each charge Force on length of wire Force on straight section of wire, length L N Current Magnetic force S Magnetic field Tue. Oct. 20, 2009 Physics 208 Lecture 14

‘Homopolar’ motor Why does the motor turn? Electric Coulomb force pushes on magnet Magnetic field pushes on current from battery Current from battery heats the magnet Current through wire produces magnetic field Tue. Oct. 20, 2009 Physics 208 Lecture 14

Electric current produces magnetic field Current (flow of electric charges ) in wire produces magnetic field. That magnetic field aligns compass needle Current Magnetic field Tue. Oct. 20, 2009 Physics 208 Lecture 14

Law of Biot-Savart B out of page Each element of current produces a contribution to the magnetic field. r  I ds dI dB r = permeability of free space r = distance from current element Tue. Oct. 20, 2009 Physics 208 Lecture 14

Magnetic field from long straight wire: Direction y What direction is the magnetic field from an infinitely-long straight wire? x I Tue. Oct. 20, 2009 Physics 208 Lecture 14

Magnetic field from a current Iron filings align with magnetic field lines Magnetic field loops around the current. Tue. Oct. 20, 2009 Physics 208 Lecture 14

Forces between currents Which of these pairs of currents will attract each other? A A & C B A & B Do demo of current carrying wires forcing each other apart. A B C Tue. Oct. 28, 2008 Physics 208, Lecture 17

Force between current-carrying wires Attractive for parallel currents. Repulsive for antiparallel currents Tue. Oct. 28, 2008 Physics 208, Lecture 17

Current dependence How does the magnitude of the B-field change if the current is doubled? y Is halved Quadruples Stays same Doubles Is quartered x I Tue. Oct. 20, 2009 Physics 208 Lecture 14

Distance dependence How does the magnitude of the B-field at 2 compare to that at 1? y 2 B2=B1 B2=2B1 B2=B1/2 B2=4B1 B2=B1/4 1 x I Tue. Oct. 20, 2009 Physics 208 Lecture 14

Why? Biot-Savart says Why B(r) 1/r instead of 1/r2 ? Small contribution from this current element. ~ independent of r Large contribution from this current element. Decreases as 1/r2 I Tue. Oct. 20, 2009 Physics 208 Lecture 14

Long straight wire All current elements produce B out of page Add them all up: r a  x Tue. Oct. 20, 2009 Physics 208 Lecture 14

Field from a circular loop Each current element produce dB All contributions add as vectors Along axis, all components cancel except for x-comp Tue. Oct. 20, 2009 Physics 208 Lecture 14

Magnetic field from loop Bz Which of these graphs best represents the magnetic field on the axis of the loop? A. z Bz B. z z x y Bz C. z Bz D. z Tue. Oct. 20, 2009 Physics 208 Lecture 14