Electricity & Magnetism Lecture 12

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Maurice Perkins
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1 Electricity & Magnetism Lecture 12 Today s Concept: Magne2c Force on Moving Charges Electricity & Magne2sm Lecture 12, Slide 1

2 Today s rants I'm struggling a fair bit with this component of the course. Got me feeling like- hkps:// and this hkps://youtu.be/ppccpglnnf0?t=1m39s

3 Comments this stuff gets fun now :) Will a magnet car move?????? Please go over cross product. What is the "sense" in these magne2c concepts? Is it the same as a vector "direc2on"? Also, can you demonstrate the right-hand rule. It is a bit abstract to "see" on a flat screen, a visual demo would be nice. etc., etc.,... Will do! Diagram of a Maglev train electrodyna

5 Magnetic Observations ar Magnets N S N S S N N S Compass Needles N S These are magnetic dipoles and behave similarly to electric dipoles Magne2c Charge? N S cut in half N S N S Electricity & Magne2sm Lecture 12, Slide 2

6 Magnetic Observations Compass needle deflected by electric current Magne2c fields created by electric currents Magne2c fields exert forces on electric currents (charges in mo2on) I V V F F I I I F F I V V Electricity & Magne2sm Lecture 12, Slide 3

7 Magnetism & Moving Charges All observa2ons are explained by two equa2ons: Today Next Week Electricity & Magne2sm Lecture 12, Slide 4

8 Cross Product Review Cross Product different from Dot Product A is a scalar; A is a vector A propor2onal to the component of parallel to A A propor2onal to the component of perpendicular to A Defini2on of A Magnitude: A sin θ Direc2on: perpendicular to plane defined by A and with sense given by right-hand-rule Tex Text Text Electricity & Magne2sm Lecture 12, Slide 5

9 Remembering Directions: The Right Hand Rule F y x qv z Electricity & Magne2sm Lecture 12, Slide 6

10 CheckPoint 2 Three points are arranged in a uniform magne2c field. The field points into the screen. A positively charged particle is at point A and is stationary. The direction of the magnetic force on the particle is A. right. left C. into screen D. out of screen E. zero Electricity & Magne2sm Lecture 12, Slide 7

11 CheckPoint 4 Three points are arranged in a uniform magne2c field. The field points into the screen. The positive charge moves from A to. The direction of the magnetic force on it is A. right. left C. into screen D. out of screen E. zero Electricity & Magne2sm Lecture 12, Slide 8

12 Cross Product Practice Protons (posi2ve charge) coming out of screen Magne2c field poin2ng down What is direc2on of force on POSITIVE charge? A) Lek ) Right C) UP D) Down E) Zero x + x + y y y x screen z Electricity & Magne2sm Lecture 12, Slide 9

13 Motion of Charge q in Uniform Field Force is perpendicular to v Speed does not change Uniform Circular Mo2on Solve for R: x x x x x x x x R x x x x v x x x x x F x x x x q q x x x x x x x x x x x x x x v v F F q x x x x x x x Uniform into page F v q Electricity & Magne2sm Lecture 12, Slide 10

14 17 miles diameter LHC mv p R= = q q Electricity & Magne4sm Lecture 12, Slide 13

15 CheckPoint 6 The drawing shows the top view of two interconnected chambers. Each chamber has a unique magne2c field. A posi2vely charged par2cle is fired into chamber 1, and observed to follow the dashed path shown in the figure. What is the direc2on of the magne2c field in chamber 1? A. up. down Confusion? C. into page D. out of page E. Zero Electricity & Magne2sm Lecture 12, Slide 11

CheckPoint 8 The drawing shows the top view of two

1, and observed to follow the dashed path shown in

Compare the magnitude of the magne2c field in

16 CheckPoint 8 The drawing shows the top view of two interconnected chambers. Each chamber has a unique magne2c field. A posi2vely charged par2cle is fired into chamber 1, and observed to follow the dashed path shown in the figure. Compare the magnitude of the magne2c field in chamber 1 to the magnitude of the magne2c field in chamber 2. A. 1 > 2. 1 = 2 C. 1 < 2 Electricity & Magne2sm Lecture 12, Slide 12

17 Calculation A par2cle of charge q and mass m is accelerated from rest by an electric field E through a distance d and enters and exits a region containing a constant magne2c field at the points shown. Assume q,m,e,d, and x 0 are known. What is? Conceptual Analysis What do we need to know to solve this problem? enters here A) Lorentz Force Law ) E field defini2on C) V defini2on q,m E d x 0 /2 exits here x 0 D) Conserva2on of Energy/Newton s Laws E) All of the above Electricity & Magne2sm Lecture 12, Slide 13

18 Calculation A par2cle of charge q and mass m is accelerated from rest by an electric field E through a distance d and enters and exits a region containing a constant magne2c field at the points shown. Assume q,m,e,d, and x 0 are known. What is? Strategic Analysis Calculate v, the velocity of the par2cle as it enters the magne2c field Use Lorentz Force equa2on to determine the path in the field as a func2on of Apply the entrance-exit informa2on to determine q,m E d enters here x 0 /2 exits here x 0 Electricity & Magne2sm Lecture 12, Slide 14

19 Calculation A par2cle of charge q and mass m is accelerated from rest by an electric field E through a distance d and enters and exits a region containing a constant magne2c field at the points shown. Assume q,m,e,d, and x 0 are known. What is? enters here What is v 0, the speed of the par2cle as it enters the magne2c field? q,m E d x 0 /2 exits here x 0 A C D E Electricity & Magne2sm Lecture 12, Slide 15

20 Calculation A par2cle of charge q and mass m is accelerated from rest by an electric field E through a distance d and enters and exits a region containing a constant magne2c field at the points shown. Assume q,m,e,d, and x 0 are known. What is? What is the path of the par2cle as it moves through the magne2c field? q,m A C E d enters here x 0 /2 exits here x 0 Electricity & Magne2sm Lecture 12, Slide 16

21 Calculation A par2cle of charge q and mass m is accelerated from rest by an electric field E through a distance d and enters and exits a region containing a constant magne2c field at the points shown. Assume q,m,e,d, and x 0 are known. What is? What is the radius of path of par2cle? q,m E d enters here x 0 /2 X X X X X X X X X exits here x 0 A C D E Why? R x o /2 For D, we don t know yet. Electricity & Magne2sm Lecture 12, Slide 17

22 Calculation A par2cle of charge q and mass m is accelerated from rest by an electric field E through a distance d and enters and exits a region containing a constant magne2c field at the points shown. Assume q,m,e,d, and x 0 are known. What is? q,m E d enters here x 0 /2 X X X X X X X X X exits here x 0 A C D E Electricity & Magne2sm Lecture 12, Slide 18

23 Follow-Up A par2cle of charge q and mass m is accelerated from rest by an electric field E through a distance d and enters and exits a region containing a constant magne2c field at the points shown. Assume q,m,e,d, and x 0 are known. d X X X X X X X X X What is? enters here Suppose the charge of the par2cle is doubled (Q = 2q),while keeping the mass constant. How does the path of the par2cle change? q,m E x 0 /2 exits here x 0 A C Electricity & Magne2sm Lecture 12, Slide 19

24 Follow-Up A par2cle of charge q and mass m is accelerated from rest by an electric field E through a distance d and enters and exits a region containing a constant magne2c field at the points shown. Assume q,m,e,d, and x 0 are known. What is? enters here Suppose the charge of the par2cle is doubled (Q = 2q),while keeping the mass constant. How does the path of the par2cle change? q,m E d x 0 /2 X X X X X X X X X exits here x 0 How does v, the new velocity at the entrance, compare to the original velocity v 0? A C D E Electricity & Magne2sm Lecture 12, Slide 20

25 Follow-Up A par2cle of charge q and mass m is accelerated from rest by an electric field E through a distance d and enters and exits a region containing a constant magne2c field at the points shown. Assume q,m,e,d, and x 0 are known. What is? enters here Suppose the charge of the par2cle is doubled (Q = 2q),while keeping the mass constant. How does the path of the par2cle change? q,m E d x 0 /2 X X X X X X X X X exits here x 0 How does F, the magnitude of the new force at the entrance, compare to F 0, the magnitude of the original force? A C D E Electricity & Magne2sm Lecture 12, Slide 21

26 Follow-Up A par2cle of charge q and mass m is accelerated from rest by an electric field E through a distance d and enters and exits a region containing a constant magne2c field at the points shown. Assume q,m,e,d, and x 0 are known. What is? enters here Suppose the charge of the par2cle is doubled (Q = 2q),while keeping the mass constant. How does the path of the par2cle change? q,m E d x 0 /2 X X X X X X X X X exits here x 0 How does R, the radius of curvature of the path, compare to R 0, the radius of curvature of the original path? A C D E Electricity & Magne2sm Lecture 12, Slide 22

27 mv 2 R = F R = mv2 R = m2v2 0 2 p 2F 0 = mv2 0 p 2F0 = 1 p 2 R 0 F

Physics 2112 Unit 12

Physics 2112 Unit 12 Today s Concept: Magnetic Force on Moving Charges F qv B Unit 12, Slide 1 Where we are E fields B fields Stuff You asked about.. This is crazy. But also really cool. What is that "K"