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Physics 102: Lecture 08 Review, Sunday Feb. 17 3 PM, 141 Loomis • • I will go over a past exam Vote for which exam a) b) c) d) e) Fall 2007 Spring 2007 Fall 2006 Spring 2006 Fall 2005 Today’s Lecture: Magnetism This material is NOT on exam 1 • • Magnetic fields Magnetic force on charged particles Magnets are Cool! • North Pole and South Pole - – Opposites Attract – Likes Repel + • Magnetic Field Lines – Arrows give direction – Density gives strength – Looks like dipole! Lets Break it! 15 S N S N S N Field Lines of Bar Magnet S N Magnetic field lines don’t start or stop. There are no magnetic charges (monopoles) 18 Preflight 8.1 1 Which drawing shows the correct field lines for a bar magnet? (1) 10% (2) 30% S N S N S N 2 (3) 60% • Magnetic field lines are continuous • Arrows go from N to S outside the magnet (S to N inside). 3 The Earth is a Magnet S N Comparison: Electric Field Lines vs. Magnetic Field Lines • Similarities – Density gives strength – Arrow gives direction • Leave +, North • Enter -, South • Differences – Start/Stop on electric charge – No Magnetic Charge, lines are continuous! • FYI – x x x x x x x INTO Page – • • • • • • • • • OUT of Page 20 No Magnetic Charges • Magnetic Fields are created by moving electric charge! • Where is the moving charge? Orbits of electrons about nuclei Intrinsic “spin” of electrons (more important effect) 21 Magnetic Fields and Forces • Magnetic fields exert forces on moving charge • We will discuss the magnitude of the force shortly • Direction of force is given by a “right-hand rule” Direction of Magnetic Force on Moving Charges • Magnetic force is perpendicular to both B and v • Right-hand rule: – Thumb of right hand points in v direction – Orient hand so that forefinger points in B direction – Then normal to palm points in direction of F • Outward normal for + charge • Opposite for – charge B v F 25 25 Direction of Magnetic Force on Moving Charges Velocity out of page out of page B right left out of page up Force up down B v F ACT: 1) Up 2) Down 3) Right 4) Left 5) Zero 25 Direction of Magnetic Force on Moving Charges Velocity out of page out of page out of page out of page B right left up down Force up down left right B F v 25 Preflight 8.3 Each chamber has a unique magnetic field. A positively charged particle enters chamber 1 with velocity 75 m/s up, and follows the dashed trajectory. 21% 7% 9% 30% 24% 9% 2 1 v = 75 m/s q = +25 mC What is the direction of the force on the particle just as it enters region 1? 1) up Particle is moving straight upwards 2) down then veers to the right. 3) left 4) right 5) into page 6) out of page 27 Preflight 8.4 Each chamber has a unique magnetic field. A positively charged particle enters chamber 1 with velocity 75 m/s up, and follows the dashed trajectory. 17% 6% 8% 22% 20% 26% 2 1 v = 75 m/s q = +25 mC What is the direction of the magnetic field in region 1? _ 1) up 2) down v (thumb) points up, F(palm) points right: so B(fingers) must point out. 3) left _ 4) right 5) into page 6) out of page 27 ACT: 2 Chambers Each chamber has a unique magnetic field. A positively charged particle enters chamber 1 with velocity 75 m/s up, and follows the dashed trajectory. 2 1 v = 75 m/s q = +25 mC What is the direction of the magnetic field in region 2? A) down v (thumb) points right, F(palm) points B) left up, B(fingers) point in. C) right D) into page E) out of page 29 Magnitude of Magnetic Force on Moving Charges • The magnetic force on a charge depends on the magnitude of the charge, its velocity, and the magnetic field. F = q v B sin(q) – Direction from RHR V q B • Thumb (v), fingers (B), palm (F) – Note if v is parallel to B then F=0 30 ACT: Moving Charges The three charges below have equal charge and speed, but are traveling in different directions in a uniform magnetic field. 1) Which particle experiences the greatest magnetic force? A) 1 B) 2 C) 3 D) All Same F = q v B sin(q) 2) The force on particle 3 is in the same direction as the force on particle 1. A) True B) False B 3 Thumb (v), fingers (B), palm (F) into page! 2 1 33 Comparison Electric vs. Magnetic Source: Act on: Magnitude: Direction: Electric Magnetic Charges Charges F = Eq Parallel to E Moving Charges Moving Charges F = q v B sin(q) Perpendicular to v,B 34 Velocity Selector Determine magnitude and direction of magnetic field such that a positively charged particle with initial velocity v travels straight through and exits the other side. FB E v FE Electric force is down, so need magnetic force up. By RHR, B must be into page For straight line, need |FE |= |FB | q E= q v B sin(90) B = E/v What direction should B point if you want to select negative charges? FE would be up so FB must be down. A) Into Page B) Out of page C) Left 38 D) Right Motion of Q in uniform B field • Force is perpendicular to B,v – B does no work! (W=F d cos q ) x x x – Speed is constant (W=D K.E. ) x x x x x x v – Circular motion F x x x x x x x x x x x x x x x x x F x v • Solve for R: x x x x R x x x x x x x x x x x Uniform B into page 41 Motion of Q in uniform B field • Force is perpendicular to B,v – B does no work! (W=F d cos q ) x x x – Speed is constant (W=D K.E. ) x x x x x x v – Circular motion v2 F m R v2 qvBsin(q ) m R F x x x x x x x x x x x x x x x x x F x v • Solve for R: x x x x R x x x x x x x x x x x Uniform B into page mv R qB 41 Preflight 8.6 Each chamber has a unique magnetic field. A positively charged particle enters chamber 1 with velocity v1= 75 m/s up, and follows the dashed trajectory. 2 1 v = 75 m/s q = +25 mC What is the speed of the particle when it leaves chamber 2? 17% 1) v2 < v1 46% 2) v2 = v1 36% 3) v2 > v1 Magnetic force is always perpendicular to velocity, 43 so it changes direction, not speed of particle. Preflight 8.8 Each chamber has a unique magnetic field. A positively charged particle enters chamber 1 with velocity v1= 75 m/s up, and follows the dashed trajectory. 2 1 v = 75 m/s q = +25 mC Compare the magnitude of the magnetic field in chambers 1 and 2 37% 1) B1 > B2 38% 2) B1 = B2. 26% 3) B1 < B2 mv R qB Larger B, greater force, smaller R 45 ACT Each chamber has a unique magnetic field. A positively charged particle enters chamber 1 with velocity v1= 75 m/s up, and follows the dashed trajectory. 2 1 v = 75 m/s q = ?? mC A second particle with mass 2m enters the chamber and follows the same path as the particle with mass m and charge q=25 mC. What is its charge? 1) Q = 12.5 mC 2) Q = 25 mC mv R qB 3) Q = 50 mC 48 extra questions to try B 1. Which angle do you use to determine the magnitude of the force on the charged particle? (q1, q2 , either one). V q1 q2 Either one sin(q) = sin(180-q) 2. Below I have drawn the trajectory for two charged particles traveling through a magnetic field. Is particle 1 positive or negatively charged? Positive 3. If particles 1 and 2 have the same mass and velocity, which has the largest charge? Particle 1 x x x x 1x x x x x x x x x x x x x x x x x x x x x x x x 2 Summary • We learned about magnetic fields B • We learned about magnetic forces on moving charged particles 50