Today’s Lecture: Magnetism Physics 102: Lecture 08 Today’s Lecture: Magnetism Magnetic fields Magnetic force on charged particles 1

Magnets North Pole and South Pole Magnetic Field Lines + - North Pole and South Pole Opposites Attract Likes Repel Magnetic Field Lines Arrows give direction Density gives strength Looks like dipole! 15

The Earth is a Magnet

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)

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: Point thumb of right hand in v direction Point fingers of right hand in B direction Then out-of-palm points in the direction of F for + charge opposite to F for – charge Note: different versions by different books etc. Need a prop to show this.

Direction of Magnetic Force on Moving Charges Velocity B Force out of page right up out of page left down out of page up Do this demo with crt and bar magnet. I usually say CRT has positive charge, because – sign in direction is tough. Might find better drawing of hand here. ACT: 1) Up 2) Down 3) Right 4) Left 5) Zero

Direction of Magnetic Force on Moving Charges Velocity B Force out of page right up out of page left down out of page up out of page down left right

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. 1 2 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 2) down 3) left 4) right 5) into page 6) out of page

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. 1 2 v = 75 m/s q = +25 mC What is the direction of the magnetic field in region 1? 1) up 2) down 3) left 4) right 5) into page 6) out of page

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. 1 2 v = 75 m/s q = +25 mC What is the direction of the magnetic field in region 2? A) down B) left C) right D) into page E) out of page

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 Note if v is parallel to B then F=0 V q B

ACT: Moving Charges F = q v B sin(q) B 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 2) The force on particle 3 is in the same direction as the force on particle 1. A) True B) False F = q v B sin(q) B 3 2 1

Comparison Electric vs. Magnetic Electric Magnetic Source: Charges Moving Charges Act on: Charges Moving Charges Magnitude: F = Eq F = q v B sin(q) Direction: Parallel to E Perpendicular to v,B

Velocity Selector Example 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? A) Into Page B) Out of page C) Left D) Right FE would be up so FB must be down.

Motion of Q in uniform B field Force is perpendicular to B,v B does no work! (W=F d cos q ) Speed is constant (W=D K.E. ) Circular motion Force is perpendicular to B,v x x x x x x x v R F v F v F v F v F v F Solve for R: Work out in real time Uniform B into page 41

Motion of Q in uniform B field Force is perpendicular to B,v Force is perpendicular to B,v B does no work! (W=F d cos q ) Speed is constant (W=D K.E. ) Circular motion x x x x x x x v R F v F v F v F v F v F Solve for R: Uniform B into page

Preflight 8.6 1) v2 < v1 2) v2 = v1 3) v2 > v1 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. 1 2 v = 75 m/s q = +25 mC What is the speed of the particle when it leaves chamber 2? 1) v2 < v1 2) v2 = v1 3) v2 > v1

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. 1 2 v = 75 m/s q = +25 mC Compare the magnitude of the magnetic field in chambers 1 and 2 1) B1 > B2 2) B1 = B2. 3) B1 < B2

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. 1 2 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 3) Q = 50 mC 48

extra questions to try B V 1 x x x x x x x 2 Which angle do you use to determine the magnitude of the force on the charged particle? (q1, q2 , either one). Below I have drawn the trajectory for two charged particles traveling through a magnetic field. Is particle 1 positive or negatively charged? If particles 1 and 2 have the same mass and velocity, which has the largest charge? V q1 q2 1 x x x x x x x 2

Summary We learned about magnetic fields B We learned about magnetic forces on moving charged particles